3^/0 


DE 


No.     2 


»N 


COMPLIMENTS 

204  Pl^E  STRECT 
SAH   FRANCISCO. 


A 


MENTAL  ARITHMETIC 


BT 

WILLIAM   J.    MILNE,   Ph.D.,  LL.D. 

PRESIDENT   OF  NEW  YORK  STATE    NORMAL  COLLEGE,   ALBANY,   N.Y. 


oXKo 


NEW  YORK  •:•  CINCINNATI  •:•  CHICAGO 

AMERICAN    BOOK    COMPANY 


dMot 
Mb- 


Copyright,  1897,  by 
AMERICAN  BOOK  COMPANY 


MILNE'S  MENTAL  ARITH. 
TC-P14 

EDUCATION  DEFT* 


GUC 


PREFACE 


There  are  many  who  believe  that  Mental  Arithmetic 
is  one  of  the  most  valuable  studies  in  a  school  cur- 
riculum. There  can  be  no  doubt  that  if  the  subject 
is  properly  taught  it  develops  a  habit  of  concentration 
of  mind,  which  is  one  of  the  most  desirable  ends  to 
be  attained  by  any  scheme  of  education.  This  habit 
is  not  acquired,  however,  by  constantly  performing 
operations  with  small  numbers  or  by  solving  many 
easy  problems  which  require  but  little  mental  effort, 
but  rather  by  working  examples  of  gradually  increas- 
ing difficulty,  until  the  pupil  is  enabled  with  effort  to 
solve  problems  whose  solution  might  seem  to  be  almost 
impossible,  without  resort  to  ciphering.  This  habit 
of  concentration,  when  once  it  has  become  established, 
makes  the  acquisition  of  knowledge  rapid  and  delight- 
ful, and  the  development  of  intellectual  power  notice- 
ably great. 

The  plan  adopted  in  this  book  contemplates  not 
only  the  attainment  of  this  end,  but  also  another  object 
of  equal  importance,  —  the  development  of  the  reason- 
ing faculty.     The  problems  are  arranged  upon  a  pro- 

5415C3 


4  PREFACE 

gressive  plan,  and  the  pupil  is  guided  by  explanations 
and  suggestions  until  he  is  able  to  devise  methods 
of  solution  for  himself.  The  book  thus  follows  the 
method  of  development  which  has  proved  so  success- 
ful in  the  author's  other  works. 

It  will  be  seen  at  once  that  the  book  is  not  a 
collection  of  easy  problems  designed  to  give  the  stu- 
dent practice  in  the  simple  processes  of  arithmetic, 
nor  is  it  an  exercise  book  to  accompany  a  work  on 
written  arithmetic.  It  may  be  used  with  profit  to 
supplement  such  a  work,  and  it  gives,  also,  abundant 
drill  in  computing;  but  it  constitutes  in  itself  an 
independent  book,  furnishing  such  a  thorough  course 
in  arithmetic,  that  it  will  give  to  pupils  who  master 
it  not  only  more  than  common  skill  in  computing, 
and  more  than  ordinary  ability  in  -reasoning,  but  also 
a  firm  grasp  of  the  general  principles  of  the  science. 

W.  J.  M. 


CONTENTS 


PAGE 

Addition 

►        • 

7 

Subtraction 

, 

.      17 

Multiplication      . 

.      28 

Division 

.      36 

Fractions 

.      44 

Denominate  Numbers  . 

.     109 

Percentage    

.    125 

Miscellaneous  Problems    . 

.     150 

Tables  of  Denominate  Numbers 

.     173 

MENTAL  ARITHMETIC 


o>*Ko 


ADDITION 


1.   1.  A  boy  has  2  cents  in  one  pocket  and  1  cent  in 
another  pocket.     How  many  cents  has  he  ? 

2.  I  see  2  birds  on  a  fence  and  2  birds  on  the  ground. 
How  many  birds  do  I  see  ? 

3.  A  boy  ate  2  apples  and  had  3  apples  left.     How 
many  had  he  at  first  ? 

4.  George  paid  3  cents  for  his  lunch  and  had  3  cents 
left.     How  much  had  he  at  first  ? 

5.  I  walked  4  miles  the  first  hour,  and  3  miles  the 
second.     How  far  did  I  walk  in  the  two  hours  ? 

6.  An  apple  cost  3  cents  and  an  orange  5  cents. 
How  much  did  both  cost  ? 

7.  Kate  paid  5  cents  for  some  ribbon  and  4  cents 
for  candy.     How  much  did  she  pay  for  both  ? 

8.  Mary  had  5  books  and  bought  5  more.     How 
many  had  she  then  ? 

9.  There  were  6  lilies  on  one  stalk  and  5  on  another. 
How  many  lilies  were  there  on  both  stalks  ? 

10.    In   one   room   there   were   5   windows    and    in 
another  7.     How  many  were  there  in  both  rooms  ? 

7 


?•.::/:  '.':  £•'•]  I ..:  /'•  Addition 

11.  A  pound  of  sugar  cost  7  cents,  and  a  quart  of 
beans  6  cents.     How  much  did  both  cost  ? 

12.  I  bought  at  one  time  8  quarts  of  berries  and  at 
another  7  quarts.     How  many  quarts  did  I  buy  ? 

13.  There  were  9  fish  in  an  aquarium,  and  6  more 
were  put  in.     How  many  were  there  in  the  aquarium  ? 

14.  Arthur  had  9  marbles,  and  Louis  6.     How  many 
had  both  ? 

15.  Maud    spelled    9   words   and   missed   8.      How 
many  words  were  given  her  to  spell  ? 

In  the  following  examples  add  the  given  number  to 
each  of  the  succeeding  numbers. 

16.  Add3 

to  8,  5,  4,  6,  8,  2,  9,  7,  6,  8,  5,  4,  3,  8,  5,  7,  6. 

17.  Add  7     . 

to  3,  7,  4,  3,  9,  4,  8,  6,  9,  2,  6,  8,  5,  7,  4,  3,  9. 

18.  Add  9 

to  6,  3,  5,  7,  6,  8,  9,  3,  2,  5,  8,  4,  7,  6,  8,  4,  5. 

19.  Add  6 

to  5,  3,  8,  4,  7,  8,  5,  6,  8,  4,  2,  9,  8,  7,  4,  5,  6. 

20.  Add  8 

to  5,  8,  2,  7,  9,  6,  3,  5,  8,  4,  6,  3,  9,  8,  7,  6,  5. 

21.  Add  5 

to  8,  3,  9,  4,  7,  6,  3,  8,  2,  5,  9,  7,  6,  4,  3,  2,  8. 

22.  Add  4 

to  6,  8,  5,  3,  6,  7,  9,  2,  4,  8,  5,  3,  6,  8,  4,  2,  6. 

23.  Add  7 

to  5,  9,  3,  7,  6,  8,  4,  5,  4,  9,  3,  4,  7,  8,  6,  1,  8. 


ADDITION  9 

24.  Add  6 

to  8,  3,  2,  9,  5,  8,  3,  6,  7,  8,  3,  9,  7,  4,  2,  9,  5. 

25.  Add  3 

to  7,  6,  5,  4,  9,  3,  8,  6,  2,  7,  9,  3,  4,  5,  8,  2,  7. 

26.  Add  9 

to  6,  3,  7,  8,  5,  9,  2,  8,  6,  3,  5,  4,  3,  8,  6,  5,  3. 

27.  Add  5 

to  7,  8,  4,  3,  6,  8,  7,  9,  6,  3,  7,  2,  8,  6,  5,  4,  9. 

28.  Add  8 

to  4,  3,  8,  6,  7,  5,  3,  2,  8,  6,  4,  8,  5,  9,  3,  7,  6. 

29.  Add  7 

to  5,  4,  7,  6,  3,  8,  4,  9,  5,  7,  2,  8,  5,  9,  3,  1,  6. 

30.  Add  4 

to  9,  5,  4,  3,  9,  7,  6,  8,  4,  3,  9,  7,  5,  6,  1,  8,  2. 

31.  Add  6 

to  6,  5,  8,  7,  9,  6,  8,  5,  9,  7,  4,  3,  2,  8,  2,  7,  9. 

2.  1.   A  pound  of  rice  cost  8  cents  and  a  can  of  toma- 
toes 9  cents.     Find  the  cost  of  both. 

2.  Charles  paid  9  cents  for  a  ball  and  10  cents  for  a 
bat.     How  much  did  they  both  cost  ? 

3.  A  paid  $9  on  a  debt  and  still  owed  $11.  How 
much  did  he  owe  at  first  ? 

4.  A  quart  of  cranberries  cost  6  cents  and  a  quart 
of  peaches  12  cents.     How  much  did  both  cost  ? 

5.  Mary  answered  8  geography  questions  and  12 
history  questions.  How  many  questions  did  she  an- 
swer? 


10  ADDITION 

6.  There  were  9  eggs  in  one  nest  and  12  in  another. 
How  many  eggs  were  there  in  both  ? 

7.  If  12  oranges  were  bought  at  one  time  and  11  at 
another,  how  many  were  bought  altogether  ? 

8.  A  farmer  sold  9  calves  to  one  man  and  11  to 
another.     How  many  did  he  sell  to  both  ? 

9.  George  walked  11  miles  and  rode  10  miles.     How 
far  did  he  go  ? 

10.  After  paying  7  cents  for  a  top,  Henry  has  12 
cents  left.     How  much  had  he  at  first  ? 

11.  Milk  is  6  cents  per  quart  and  cream  12  cents. 
How  much  will  a  quart  of  each  cost  ? 

12.  My  brother  caught  a  fish  weighing  8  pounds, 
and  my  cousin  another  weighing  4  pounds  more  than 
the  first.     How  much  did  both  weigh  ? 

13.  One  number  is  9  and  another  is  3  more  than  9. 
Find  their  sum. 

14.  It  takes  $  5  more  to  pay  my  grocer  than  it  does 
to  pay  my  butcher.  If  I  owe  the  butcher  $  7,  how  much 
do  I  owe  both? 

15.  Henry  paid  5  dimes  for  a  pair  of  skates  and  11 
dimes  for  a  hat.     How  much  did  both  cost  him  ? 

16.  Add  to  each  of  the  following  numbers  each  of 
the  numbers  given  in  the  rows  marked  (a),  (6),  (<?),  etc.: 

6,  5,  8,  3,  2,  4,  9,  7,  5,  4,  8,  6,  3. 

(a)  3,  5,  6,  8,  2,  9,  5,  6,  8,  4,  5,  6,  7,  3,  9,  2. 

(6)  8,  6,  3,  9,  5,  8,  4,  6,  3,  5,  9,  2,  4,  8,  1,  7. 

(>)  4,  2,  7,  6,  3,  9,  5,  8,  1,  7,  6,  5,  3,  8,  4,  6. 

(d)  5,  8,  3,  9,  4,  2,  7,  3,  9,  5,  8,  7,  6,  2,  5,  4. 

(e)  7,  5,  4,  3,  6,  1,  8,  5,  3,  2,  4,  9,  7,  8,  4,  6. 


ADDITION  11 

3.   1.    What  is  the  sum  of  8  and  5  ?    7  and  8  ?     9  and 
7?     6  and  9?     5  and  7?     9  and  8?     4  and  9? 

2.  What  is  the  sum  of  9  and  5?     9  and  4?     8  and 
6  ?     9  and  9  ?     8  and  7  ?     3  and  8  ? 

3.  What  is  the  sum  of  11  and  9?     7  and  11  ?     11 
and  5?    4  and  11?     11  and  6?     8  and  11  ? 

4.  Abram  earned  12  cents  on  Monday  and  9  cents 
on  Tuesday.     How  much  did  he  earn  in  the  two  days  ? 

5.  I  expended  8  cents  and  15  cents  for  two  books. 
How  much  did  I  expend  for  both  ? 

6.  How  much  is  8  and  6?     18  and  6?     28  and  6? 
38  and  6?     58  and  6?     88  and  6?     78  and  6? 

7.  What  is  the  sum  of  8  and  9?     18  and  9?     28 
and  9?     38  and  9?     88  and  9?     58  and  9?     78  and  9? 

8.  How  much  is  3  and  8?     13  and  8?     33  and  8? 
53  and  8  ?     93  and  8  ?     43  and  8  ?     73  and  8  ? 

9.  My  hat  cost  63  cents,  and  my  hat  band  8  cents. 
How  much  did  both  cost  ? 

10.  I  paid  75  cents  for  a  ball  and  9  cents  for  a  bat. 
Find  the  cost  of  both. 

11.  How  much  is  57  and  8?     37  and  8?     17  and  8? 
47  and  8?     97  and  8?     67  and  8?     27  and  8? 

12.  What  is  the  sum  of  4  and  8?     44  and  8?     74 
and  8?     34  and  8?     14  and  8?     84  and  8? 

13.  What  is  the  sum  of  18  and  8  ?     28  and  8  ?     58 
and  8  ?     38  and  8  ?     88  and  8  ?     68  and  8  ? 

14.  How  much  is  6  and  9  ?     9  and  56  ?     59  and  6  ? 
76  and  9  ?     89  and  6  ?     39  and  6  ?     46  and  9  ? 


12  ADDITION 

15.    Add   to  each   of  the   following  numbers,  each 
number  given  in  the  rows  below  them  : 

4,  5,  8,  7,  3,  2,  9,  6,  5,  8,  4,  7,  9,  10. 

(a)  7,  47,  37,  87,  27,  97,  77,  17,  57,  67. 

(6)  9,  29,  59,  89,  49,  19,  39,  99,  69,  79. 

00  6,  66,  56,  86,  36,  76,  46,  26,  96,  16. 

((f)  5,  35,  85,  25,  45,  95,  65,  55,  15,  75. 

(e)  4,  14,  24,  34,  44,  54,  64,  74,  84,  94. 

.    (/)  8,  58,  18,  48,  28,  38,  78,  98,  68,  88. 

(£)  3,  23,  53,  93,  43,  73,  13,  83,  33,  63. 

4.   1.    What  is  the  sum  of  6  and  5  and  9? 

2.  How  many  are  9  and  11  and  8  ? 

3.  How  many  are  8  and  8  and  12  ?     7  and  12  and 
10?     6  and  9  and  11?     7  and  6  and  12? 

4.  What  is  the  sum  of  12  and  11  and  8  ?    11  and  11 
and  6?     12  and  5  and  12?     9  and  7  and  9? 

5.  How  many  are  5  and  7  and  9  and  6  ?     8  and  6 
and  10  and  5?     6  and  12  and  8  and  7  ? 

6.  What  is  the  sum  of  28  and  10  ?    47  and  20  ?    67 
and  30  ?     25  and  20  ?     33  and  60  ? 

7.  How  many  are  44  and  20  ?     23  and  20  ?     59  and 
20?     89  and  40?     54  and  30? 

8.  How  many  are  47  and  20  and  9?    39  and  30  and 
8?     64  and  20  and  7? 

9.  What  is  the  sum  of  46  and  37? 

Solution  :  —  The  sum  of  46  and  37  is  equal  to  the  sura  of  46 
and  30  and  7.     The  sum  of  46  and  30  is  76 ;  76  and  7  is  83. 
Therefore,  the  sum  of  46  and  37  is  83. 

10.    How  many  are  48  and  39  ?     29  and  36  ?     67  and 
23?    44  and  36?     38  and  46? 


ADDITION  13 

11.  How  many  are  77  and  63  ?  84  and  55  ?  96  and 
78?     99  and  87?     58  and  85? 

12.  What  is  the  snm  of  79  and  28?  86  and  43? 
47  and  98  ?     68  and  87  ?     74  and  95  ? 

13.  How  many  are  23  and  69  ?  45  and  46  ?  37  and 
35?     43  and  29?     54  and  39? 

14.  How  many  are  37  and  48  and  20?  43  and  66 
and  40  ?     87  and  28  and  10  ?     65  and  39  and  50  ? 

15.  How  many  are  23  and  44  and  65  ?  68  and  27 
and  39  ?     46  and  75  and  37  ?     61  and  75  and  49  ? 

5.  1.  A  boy  paid  5  cents  for  an  orange,  8  cents  for  a 
top,  and  9  cents  for  some  candy.  How  much  did  he 
pay  for  all? 

Solution  :  —  He  paid  for  all  the  sum  of  5  cents,  8  cents,  and  9 
cents,  which  is  22  cents. 

2.  Harry  had  19  cents  and  earned  9  cents  more. 
How  much  had  he  then? 

3.  In  a  certain  class  there  are  24  boys  and  25  girls. 
How  many  pupils  are  there  in  the  class  ? 

4.  In  an  orchard  there  are  36  apple  trees,  19  pear 
trees,  and  40  peach  trees.  How  many  trees  are  there 
in  the  orchard  ? 

5.  One  boy  caught  44  fish,  another  37,  and  a  third 
30.     How  many  fish  were  caught  by  the  boys? 

6.  A  man  is  46  years  old,  his  wife  38,  and  their  son 
12.     What  is  the  sum  of  their  ages  ? 

7.  I  paid  60  cents  for  some  plums,  75  cents  for  some 
peaches,  and  50  cents  for  some  apricots.  How  much 
did  they  all  cost  ? 


14  ADDITION 

8.  The  distance  from  Auburn  to  Glendale  is  30 
miles,  from  Glendale  to  Roseton  18  miles,  and  from 
Roseton  to  Saybrook  20  miles.  How  far  is  it  from 
Auburn  to  Saybrook? 

9.  England  and  Wales  contain  58  thousand  square 
miles  of  land,  Ireland  33  thousand,  and  Scotland  30 
thousand.     What  is  the  combined  area? 

10.  A  girl  had  3  pieces  of  ribbon.  Their  lengths 
were  27  inches,  49  inches,  and  30  inches.  How  many 
inches  of  ribbon  had  she  ? 

11.  One  fish  weighed  24  pounds,  another  36  pounds, 
and  a  third  40  pounds.     How  much  did  they  all  weigh  ? 

12.  A  geography  cost  68  cents,  an  arithmetic  37 
cents,  and  a  grammar  30  cents.     Find  the  cost  of  all. 

13.  A  farm  contains  39  acres  of  woodland  and  75 
acres  of  cleared  land.  How  many  acres  are  there  in 
the  farm? 

14.  A  miller  paid  $65  for  wheat,  $  39  for  rye,  and 
$40  for  oats.     How  much  did  all  cost? 

15.  A  drover  bought  at  different  times  48  horses, 
66  horses,  30  horses,  and  19  horses.  How  many  horses 
did  he  buy? 

16.  A  merchant  sold  to  a  customer  3  pieces  of  cloth. 
One  contained  38  yards,  the  second  42  yards,  and  the 
third  50  yards.     How  many  yards  of  cloth  did  he  sell  ? 

17.  A  boy  bought  65  Brazil  nuts,  83  English  walnuts, 
and  80  almonds.     How  many  nuts  did  he  buy? 

18.  A  horse  cost  $  85,  and  a  carriage  $  25  more  than 
the  horse.     What  was  the  cost  of  both  ? 


ADDITION  15 

19.  How  high  is  a  tree  that  is  75  feet  from  the 
ground  to  the  first  limb,  and  87  feet  from  the  first  limb 
to  the  top? 

20.  From  A  to  B  the  road  extends  37  miles  up  hill, 
29  miles  down  hill,  and  40  miles  on  a  level.  How  far 
is  it  from  A  to  B  ? 

21.  A  farmer  has  87  sheep,  29  cows,  and  30  horses. 
How  many  animals  has  he  ? 

22.  A  miller  shipped  to  a  customer  at  one  time  43 
barrels  of  flour,  at  another  time  58  barrels,  and  made  a 
third  shipment  of  20  barrels.  How  many  barrels  were 
shipped  ? 

23.  A  horse  cost  $40  more  than  a  cow.  How  much 
did  both  cost  if  $48  was  paid  for  the  cow? 

24.  A  young  man  entered  the  navy  when  he  was  19 
years  old.  That  was  23  years  ago.  How  old  is  he 
now? 

25.  I  bought  a  wagon  for  $65,  I  paid  $12  to  have  it 
repaired,  then  sold  it  so  as  to  gain  $17.  How  much 
did  I  get  for  it  ? 

26.  A  merchant  deposited  in  a  bank  $25  more  on 
Tuesday  than  on  Monday.  If  Monday's  deposit  was 
$65^  what  was  the  amount  of  both  deposits? 

27.  Mr.  Brown,  whose  farm  consists  of  87  acres, 
buys  an  adjoining  farm  that  contains  20  acres  more 
than  his  own  farm.  How  many  acres  does,  he  have 
after  the  purchase  ? 

28.  A  boy  rode  a  bicycle  28  miles  one  day  and  12 
miles  farther  the  second  day  than  the  first.  How  far 
did  he  ride  during  the  two  days  ? 


16  ADDITION 

29.  A  silk  dress  cost  $45,  a  muff  cost  $10  more  than 
the  dress,  and  a  cloak  cost  as  much  as  the  dress  and 
muff.     Find  the  cost  of  all. 

30.  My  horse  cost  $  125  and  my  carriage  $  75.  I  sold 
the  horse  so  as  to  gain  $40  dollars  on  the  cost  of  both 
horse  and  carriage.  How  much  did  I  receive  for  the 
horse  ? 

31.  My  father  is  11  years  older  than  my  mother. 
They  were  married  20  years  ago,  when  my  mother  was 
23.     What  is  the  sum  of  their  ages  now  ? 

32.  Arthur  weighs  68  pounds,  his  brother  weighs 
12  pounds  more  than  he,  and  their  father  weighs  20 
pounds  more  than  the  boys  together.  Find  the  sum 
of  all  their  weights. 

33.  When  I  paid  bills  of  96  cents  and  79  cents,  I 
had  a  quarter  of  a  dollar  and  two  dimes  left.  How 
much  had  I  at  first  ? 

34.  Twenty-five  minutes  ago  it  was  a  quarter  to  ten. 
What  time  will  it  be  one  hour  and  10  minutes  hence? 

35.  A  man  traveled  47  miles  by  rail,  38  miles  by 
stage,  and  15  miles  on  foot.     How  far  did  he  travel  ? 

36.  Harry  went  to  the  well  for  water  three  times, 
bringing  14  quarts  the  first  time,  19  quarts  the  second 
time,  and  17  quarts  the  third  time.  How  many  quarts 
'of  water  did  he  bring  ? 

37.  After  Mr.  Allen  had  sold  75  bushels  of  wheat  to 
one  man  and  83  to  another  he  had  36  bushels  left. 
How  many  bushels  did  he  raise  ? 

38.  A  farmer  sold  27  sheep,  lost  16,  and  had  84  left. 
How  many  had  he  at  first  ? 


SUBTRACTION 


6.    1.    Howard  had  8  marbles  and   lost  3  of  them. 
How  many  had  he  left? 

2.  A  boy  who  had  12  cents  paid  5  cents  for  an 
orange.     How  many  cents  had  he  left? 

3.  If  11  birds  alighted  on  a  tree,  and  4  of  them  flew 
away,  how  many  were  left  on  the  tree  ? 

4.  John  is  13  years  old,  and  his  brother  is  5  years 
younger.     How  old  is  his  brother  ? 

5.  Mary  had  a  piece  of  ribbon  15  inches  long  and 
gave  her  sister  a  piece  of  it  8  inches  long.  How  many 
inches  of  ribbon  had  she  left? 

6.  The  sum  of  two  numbers  is  14.  If  one  of  them 
is  6,  what  is  the  other? 

7.  Harry  is  now  16  years  old.  How  old  was  he  7 
years  ago  ? 

8.  By  selling  a  bat  for  17  cents,  Harry  gained  8 
cents.     How  much  did  it  cost  him  ? 

9.  A  merchant  has  16  barrels  of  flour,  and  sells  all 
but  8  of  them.     How  many  does  he  sell? 

10.  Eggs  bought  for  10  cents  a  dozen  are  sold  for 
18  cents  a  dozen.     How  much  is  gained  on  a  dozen  ? 

11.  Louis  lost  some  marbles  and  has  9  left.     If  he 
had  17  at  first,  how  many  did  he  lose  ? 

MILNE   MENTAL  —  2  17 


18  SUBTRACTION 

12.  A  man  owed  his  grocer  $15  and  paid  $7  of  the 
debt.     How  much  had  he  yet  to  pay  ? 

13.  To  a  man  whom  I  owed  $  16, 1  gave  a  ton  of  hay 
worth  $  9  and  the  rest  in  money.  How  much  money 
did  I  pay  him? 

14.  What  number  must  be  added  to  5  to  make  13  ? 

15.  A  string  15  feet  long  was  cut  into  two  pieces, 
one  of  which  was  9  feet  long.  How  long  was  the 
other  piece  ? 

16.  A  merchant  cut  9  yards  of  ribbon  from  a  piece 
containing  21  yards.     How  many  yards  were  left  ? 

17.  What  sum  of  money  must  be  added  to  $7  to 
make  $19? 

18.  James  has  $8.  How  much  more  must  he  have 
to  buy  a  suit  of  clothes  worth  $  21  ? 

19.  A  boy  raised  11  bushels  of  pop  corn,  and  sold  7 
bushels.     How  many  bushels  had  he  left  ? 

20.  A  lady  paid  $15  for  a  cloak,  and  $9  less  for  a 
hat.     How  much  did  her  hat  cost  ? 

21.  If  a  boy  earns  $15  per  month,  and  spends  $7, 
how  much  does  he  save  ? 

22.  A  man  earns  $18  per  week,  which  is  $9  more 
than  his  son  earns.     How  much  does  his  son  earn  ? 

23.  A  man  gained  $3  on  a  cow  which  he  sold  for 
$21.     How  much  did  the  cow  cost  him? 

24.  A  watch  that  cost  $18  was  sold  at  a  loss  of  $5. 
How  much  was  received  for  it? 

25.  A  man  whose  weekly  wages  were  $20,  spent  $8 
every  week.  How  much  of  his  wages  had  he  left  at 
the  end  of  each  week  ? 


SUBTRACTION  19 

26.  From  11,  10,  12,  15,  8,  6,  9,  7,  5,  12,  8,  9,  4,  13, 
subtract  3. 

27.  From  13,  18,  15,  9,  19,  20,  18,  14,  16,  17,  11,  9, 
subtract  7. 

28.  From  20,  13,  18,  10, 15,19,  21,  16, 12,  14,  17,  15, 
subtract  9. 

29.  From  12,  15,  17, 13,  9,  8, 19,  20,  16,  14,  15,  7,  11, 
subtract  6. 

30.  From  15,  12,  13,  19,  17,  11,  20,  9,  14,  18,  16,  11, 
subtract  8. 

31.  From  13,  15,  8,  12,  18,  17,  20,  11,  9,  14,  19,  16, 
subtract  5. 

32.  From  8,  13,  17,  18,  20,  15,  11,  10,  9,  16,  8,  12,  7, 
subtract  4. 

33.  From  12,  17,  9,  11,  15,  18,  20,  13,  16,  19,  14,  8, 
subtract  7. 

34.  From  15,  12,  10,  8,  11,  9,  13,  17,  19,  20,  16,  14, 
subtract  6. 

35.  From  15,  9,  13,  8,  11,  14,  10,  12,  16,  17,  20,  6,  7, 
subtract  3. 

36.  From  18,  15,  13, 17,  11, 14,  16,  21,  12,  20, 17,  19, 
subtract  9. 

37.  From  8, 12, 15,  19,  11,  14,  9,  7, 10, 13,  16,  20,  18, 
subtract  5. 

38.  From  11,  17, 13,  10,  15,  18,  21, 19,  12,  16,  14,  20, 
subtract  8. 

39.  From  15,  11,  13,  8,  12,  17,  14,  10,  19,  20,  18,  9, 
subtract  7. 

40.  From  10,  13,  17,  11,  9,  19,  12,  18,  16,  15,  8,  14, 
subtract  4. 


20  SUBTRACTION' 

7.   1.    How  much  is  17  less  10?  37  less  10?  27  less 
10?  67  less  10?  47  less  10?   ' 

2.  What  is  the  difference  between  28  and  20  ?   48 
and  20?  58  and  30?  48  and  30? 

3.  How  many  are  left  when  20  is  taken  from  36  ? 
30  from  54?  40  from  85?  60  from  97? 

4.  Take  29  from  47. 

Solution  :  —  29  is  equal  to  20  plus  9.    20  taken  from  47  leaves 
27;  9  taken  from  27  leaves  18.     Therefore  47  -  29  =  18. 

5.  Take  31  from  56;  18  from  39;  41  from  86;  16 
from  33;  28  from  53. 

6.  What  is  the  difference  between  45  and  90  ?  47 
and  80  ?  33  and  67  ?  44  and  71  ? 

7.  How  much  is  93  less  65  ?  81  less  37  ?  64  less  29  ? 
75  less  36  ? 

8.  Subtract  62  from  100;  39  from  100;  86  from  200; 
75  from  150  ;  89  from  160. 

9.  Subtract  77  from  120 ;   59  from  130  ;   67  from 
140  ;  53  from  160 ;  38  from  110. 

10.  Subtract  48  from  123 ;  55  from  121  ;    81  from 
164  ;  64  from  165  ;  91  from  146. 

11.  Subtract  43  from  121  ;    68  from    132;  52  from 
141 ;  19  from  101 ;  18  from  103. 

12.  Subtract  121  from  187  ;  135  from  196 ;  146  from 
172  ;  154  from  193  ;  119  from  187. 

13.  Take  230  from  430 ;  138  from  438;  160  from 
470;  290  from  400;  295  from  500. 

14.  Take  240  from  457 ;   360  from  477  ;    570  from 
896  ;  440  from  687  ;  325  from  575. 


SUBTRACTION  21 

8.  1.  A  farmer  has  23  turkeys  and  sells  14  of  them. 
How  many  has  he  left? 

2.  There  are  28  pupils  in  a  class  room.  How  many 
boys  are  there,  if  13  of  the  pupils  are  girls? 

3.  I  paid  $21  for  a  ton  of  hay  and  2  cords  of  wood. 
The  wood  cost  $8.     How  much  was  paid  for  the  hay? 

4.  A  boy  caught  45  fish,  but  16  of  them  were  so 
small  that  he  threw  them  back  into  the  water.  How 
many  had  he  left  ? 

5.  Mr.  Brown  borrowed  $50.  How  much  did  he 
owe  after  paying  $  23  of  the  debt  ? 

6.  A  tailor  has  a  piece  of  cloth  containing  43  yards. 
After  he  has  used  18  yards,  how  much  is  left? 

7.  A  boy  has  17  marbles  and  gets  enough  more  to 
make  36.     How  many  does  he  get  ? 

8.  A  bushel  of  wheat  cost  65  cents,  and  a  bushel  of 
rye  48  cents.  How  much  more  did  the  wheat  cost  than 
the  rye? 

9.  From  New  York  to  Philadelphia  is  90  miles. 
How  much  of  the  distance  remains  to  be  traveled  after 
48  miles  of  it  has  been  gone  over  ? 

10.  In  an  orchard  containing  119  trees,  68  are  apple 
trees.  If  the  rest  are  pear  trees,  how  many  pear  trees 
are  there  ? 

11.  At  noon  the  temperature  stood  at  88  degrees, 
and  at  midnight  at  69  degrees.  How  many  degrees 
had  it  fallen  ? 

12.  By  the  Fahrenheit  scale  the  boiling  point  of 
water  is  212  degrees,  and  the  freezing  point  32  degrees. 
What  is  the  difference  between  the  two  points  ? 


22  SUBTRACTION 

13.  A  boy  who  has  50  cents  spends  15  cents  and 
earns  25  cents.     How  much  has  he  then? 

14.  A  cistern  containing  100  gallons  of  water  dis- 
charges 35  gallons  by  one  pipe,  and  receives  85  gallons 
by  another.     How  much  water  remains  in  the  cistern  ? 

15.  Mr.  Davis  will  be  50  years  old  in  8  years.  How 
old  was  he  7  years  ago  ? 

16.  Three  boys  had  together  100  marbles.  The  first 
had  25,  the  second  35.     How  many  had  the  third? 

17.  A  fish  was  40  inches  long.  The  length  of  the 
head  was  8  inches,  and  of  the  tail  9  inches.  How  long 
was  the  body  ? 

18.  A  farmer  had  87  sheep  in  a  pasture,  and  30  of 
them  escaped.  He  succeeded  in  returning  23  of  them 
to  the  pasture.     How  many  had  he  then? 

19.  Louis  earned  two  dollars.  He  bought  a  hat  for 
65  cents,  and  a  pair  of  overshoes  for  45  cents*  How 
much  money  had  he  left? 

20.  A  merchant  has  a  hat  marked  $1.39;  he  lowers 
the  price  45  cents  and  then  gains  17  cents.  How  much 
did  it  cost  him? 

21.  A  lady  went  shopping  with  a  hundred-dollar 
bill.  She  bought  a  dress  for  $22,  a  hat  for  $9,  and  a 
cloak  for  $31.     How  much  had  she  left? 

22.  On  Monday  I  traveled  45  miles  north,  on  Tues- 
day 23  miles  south,  and  on  Wednesday  36  miles  north. 
How  far  was  I  then  from  the  place  of  starting? 

23.  A  boy  bought  a  bicycle  for  $  65.  After  expend- 
ing $11  for  repairs  he  sold  it  for  $50.  How  much  did 
the  use  of  it  cost  him  ? 


SUBTRACTION  23 

24.  A  merchant  paid  $68  for  some  goods,  $8  for 
cartage,  and  $5  for  storage.  He  sold  the  goods  for 
$100.     How  much  did  he  gain  ? 

25.  I  bought  a  horse  for  $90,  paid  $25  for  keeping 
him,  and  sold  him  for  $160.     What  was  my  gain? 

26.  The  sum  of  the  ages  of  A,  B,  and  C  is  135  years. 
A  is  35,  and  B  is  9  years  older.     How  old  is  C  ? 

27.  A  jeweler  bought  a  diamond  for  $85.  He  paid 
$9  to  have  it  set,  and  then  sold  it  for  $140.  How  much 
did  he  gain  ? 

28.  A  drover  bought  at  one  time  38  sheep  and  at 
another  time  65  sheep ;  he  sold  44  of  them.  How 
many  were  left  ? 

29.  A  boy  gathered  89  quarts  of  nuts.  He  gave 
away  15  quarts,  kept  28  quarts,  and  sold  the  rest. 
How  many  quarts  did  he  sell? 

9.  1.  How  many  are  8  +  17-9?  12-5  +  8?  13- 
9  +  12?     16  +  12-10?     14+9-12? 

2.  What  is  the  value  of  8  +  13  -  9?     14-7  +  6? 
32-20  +  9?     50-25  +  6?     18  +  17-20? 

3.  What  is  the  value  of  23  +  18  -  20  ?     17  -  11  + 
27?    41-19-9?     16+18-14?     11  +  17-13? 

4.  Howmanyare8  +  9  +  20-14?    12  +  5-3-6? 

13  +  14-9-6?     24  +  16-30?     36  +  25-31? 

5.  Find  the  value  of  :  17  -  9  +  23  ;   19  +  17  -  20  ; 

14  +  17-12;  16  +  41-17;  23  +  18-21. 

6.  Find  the  difference  between  100  and  24  +  38. 

7.  How  many  are  12  +  9  +  7  -  6  +  4  ?     18  +  17  - 
14-8?     23  +  25-20-18? 


24  SUBTRACTION 

8.  How  many  are  25  +  75-36-24?     35  +  65  - 

25  +  20?     30  +  18-12-24?  * 

9.  What  is  the  value  of  23  +  27  -  18  -  15  ?    44  + 
22-33-11?     27  +  33  -  15  +  8? 

10.  A  boy  had  45  marbles.  He  lost  17  of  them  and 
then  bought  25.     How  many  did  he  then  have  ? 

11.  From  a  tub  containing  46  pounds  of  butter,  13 
pounds  were  sold  to  one  customer  and  17  to  another. 
How  much  remained  unsold? 

12.  In  one  field  there  are  44  sheep ;  in  a  second  field 
there  are  37  ;  in  a  third  field  there  are  enough  to  make 
the  entire  number  150.  How  many  are  there  in  the 
third  field? 

13.  From  A  to  B  the  distance  is  100  miles.  A  man 
sets  out  from  A  and  travels  65  miles  of  this  distance 
and  then  returns  17  miles  along  the  same  road.  How 
far  is  he  from  B  ? 

14.  A  man  who  owes  $78  pays  at  one  time  $25  and 
at  another  time  $18.     How  much  does  he  still  owe? 

15.  John  has  $37,  Henry  has  $15  more  than  John, 
and  Arthur  has  a  sum  such  that  the  three  together 
have  $130.     How  much  has  Arthur? 

16.  How  much  change  should  I  get  from  $2  after 
paying  38  cents  for  ribbon,  50  cents  for  a  cap,  and  Q5 
cents  for  a  pair  of  gloves  ? 

17.  A  man  who  has  $45  in  his  purse  draws  his 
monthly  pay  of  $135.  After  paying  his  grocer  $28,  and 
other  bills  amounting  to  $  72,  how  much  is  left  ? 


SUBTRACTION  25 

18.  A  person  who  has  1 67  in  a  bank  deposits  $99 
more,  then  draws  out  $75.  How  much  has  he  then  in 
the  bank  ? 

19.  A  rope  100  feet  long  was  cut  into  three  pieces. 
One  piece  was  42  feet  long,  and  another  was  18  feet 
shorter.     How  long  was  the  third  piece  ? 

20.  A  lady  gave  a  merchant  a  fifty-dollar  bill  and 
two  twenty-dollar  bills.  This  money  exactly  paid  for 
a  dress  costing  $22,  a  cloak  costing  $17  more  than  the 
dress,  and  a  shawl.     How  much  did  the  shawl  cost  ? 

21.  Howard  gathered  57  quarts  of  nuts,  Edwin 
gathered  13  quarts  more  than  Howard,  and  William 
13  quarts  less  than  Howard.  How  many  quarts  did 
they  all  gather  ? 

22.  From  a  school  registering  95  boys  and  108  girls, 
there  were  absent  17  boys  and  23  girls.  How  many 
pupils  were  present? 

23.  A  man  left  home  and  traveled  the  first  day  38 
miles  and  the  second  day  43  miles.  He  then  set  out  to 
return,  traveling  the  first  day  26  miles.  How  far  had 
he  yet  to  go  ? 

24.  A  man  of  war's  crew  consisted  of  300  men.  In 
an  engagement  45  were  killed,  and  the  wounded  were 
35  more  than  the  killed.     How  many  were  unhurt  ? 

25.  By  selling  some  goods  for  $  120  a  merchant  gained 
$37.  How  much  should  he  have  received  for  the  goods 
to  have  gained  $  19  ? 

26.  A  boy  has  some  money  and  earns  48  cents  more. 
He  then  buys  a  book  for  38  cents  and  a  hat  for  62  cents, 
and  has  10  cents  left.     How  much  had  he  at  first  ? 


26  SUBTRACTION 

27.  From  A  to  B  is  150  miles.  Of  this  distance  65 
miles  is  up  grade,  and  the  distance  down  grade  is  25 
miles  less.     How  much  of  the  distance  is  level  ? 

28.  A  farmer  has  two  horses  for  sale.  One  man 
offers  him  $95  for  one  and  $135  for  the  other.  An- 
other offers  him  $105  for  one  and  $110  for  the  other. 
Which  is  the  better  offer,  and  how  much  ? 

29.  A  drover  bought  47  cows,  and  then  sold  to  one 
person  29,  and  to  another  68,  and  had  none  left.  How 
many  had  he  at  first  ? 

30.  A  man  sold  35  sheep,  then  bought  14,  and  fchen 
had  25.     How  many  had  he  at  first  ? 

31.  A  man  received  $47  for  wages.  He  paid  $16 
for  a  suit  of  clothes,  $  5  for  a  barrel  of  flour,  and  $  6  for 
a  ton  of  coal.     How  much  had  he  left  ? 

32.  A  merchant  paid  $49  for  a  quantity  of  goods 
and  $4  for  freight  and  cartage.  For  how  much  did  he 
sell  them  if  he  lost  $15? 

33.  If  a  lady  buys  thread  for  15  cents,  needles  for 
5  cents,  and  ribbon  for  36. cents,  and  gives  the  clerk 
75  cents,  how  much  change  should  he  return  ? 

34.  A  boy  having  78  cents  gave  19  cents  to  his 
brother,  7  cents  less  to  his  sister,  and  lost  4  cents. 
How  much  had  he  left  ? 

35.  From  a  bin  containing  97  bushels  of  wheat  29 
bushels  were  taken  for  seed  and  17  bushels  were  sold. 
How  many  bushels  remained  in  the  bin  ? 

36.  Roy  wishes  to  buy  a  ball  for  75  cents  and  a  bat 
for  40  cents.  He  saves  58  cents,  and  his  mother  gives 
him  25  cents.     How  much  more  does  he  need  ? 


SUBTRACTION  27 

Find  the  value  of: 

37.  25  +  18  +  37-20-5-10  +  6-7  +  13-8-4. 

38.  46  +  14-30  +  17-20  +  6-3  +  10-15  +  5-9. 

39.  81-30-21  +  45-15  +  4-20  +  8-10  +  7-12. 

40.  35  +  18-23  +  24-16  +  3  +  15-10  +  7  +  12-5. 

41.  17  +  38  +  5-18  +  22  +  7-20  +  8-15  +  7-11. 

42.  25-15  +  23  +  7-18  +  2  +  25-18-10  +  6-8. 

43.  27  +  23-10  +  18-12  +  8-4  +  20-35  +  8-10. 

44.  36-16  +  20  +  35-25-15  +  10  +  12  +  7 -10-25e 

45.  41-11  +  15  +  15-30  +  25-40  +  5  +  15-10-5. 

46.  57  +  13-35  +  10-9-8  +  12  +  15-6-7  +  8. 

47.  62  +  13-25  +  22-36  +  4  +  10  +  25-20-5  +  8. 

48.  18  +  42-20-25  +  23-13  +  24  +  16-30-8  +  9. 

49.  34  +  16  +  25-35-15  +  25-16+JL8-24  +  8  +  12. 

50.  27-7  +  20-8  +  18-10  +  24  +  16-20  +  18-4. 

51.  53-13  +  25-17  +  26-34  +  57-8  +  13  +  4-9. 

52.  62-32  +  42-55  +  23-10  +  28  +  15-3-19-7. 

53.  7i  +  i9_40  +  38-16-24  +  25-18  +  6-13-8. 

54.  83  +  17-35  +  10-15-8-20  +  32-6  +  18-9. 

55.  94-28  +  24-25-14  +  25-16  +  8-18  +  9  +  18. 

56.  65  +  15-40  +  28-24  +  13-9  +  8-12  +  16-9. 

57.  85-25  +  24-18  +  13-27  +  18  +  9-8  +  6-19. 

58.  58  +  22-28  +  13-16  +  28  +  22-31  +  9  +  8  +  6. 

59.  86  +  15-21  +  18  +  15-32  +  16-8  +  11  +  6-18 

60.  87-24  +  13-18  +  8  +  6-31-17  +  10-4-7. 

61.  28  +  32-17+41  +  6-12-5  +  14  +  13-16-11. 

62.  91-30  +  16-45  +  8  +  13-19  +  17-15  +  3  +  9. 


MULTIPLICATION 


10.   1.    At  2  cents  each,  what  is  the  cost  of  3  apples? 

2.  How  far  does  a  man  walk  in  4  hours,  at  the  rate 
of  3  miles  per  hour  ? 

3.  How  much  will  3  oranges  cost,  at  5  cents  each? 

4.  Each  side  of  a  square  is  4  rods  long.     How  far  is 
it  around  the  square  ? 

5.  If  I  burn  3  tons  of  coal  per  month,  how  much 
will  I  burn  in  6  months  ? 

6.  Henry's  steps  are  each  3  feet  in  length.     How 
far  does  he  go  in  8  steps  ? 

7.  At  5  cents  each,  how  much  must  be  paid  for 
7  oranges  ? 

8.  How  many  days  are  there  in  4  weeks  ? 

9.  A  man  gave  10  cents  to  each  of   5  children. 
How  much  did  he  give  to  all  ? 

10.  In  one  yard  there  are  3  feet.     How  many  feet 
are  there  in  12  yards? 

11.  A  horse  eats  7  quarts  of  oats  in  a  day.     How 
much  does  he  eat  per  week  ? 

12.  A  man  earns  $  8  a  day.     How  much  does  he  earn 
in  6  days? 

13.  At  6  cents  a  yard,  how  much  will  5  yards  of 
ribbon  cost? 

28 


MULTIPLICATION  29 

14.  There  are  8  quarts  in  a  peck.     How  many  quarts 
are  there  in  4  pecks? 

15.  At  9  cents  a  pound,  what  will  he  the  cost  of  a 
fish  weighing  3  pounds? 

16.  If  5  men  can  do  a  piece  of  work  in  4  days,  in 
what  time  can  one  man  do  it  ? 

17.  Multiply  3,  8,   7,  6,  5,  9,  8,  7,  6,  8,  2,  4,  5,  9,  6, 

8,  3,  4,  10, 11,  12, 

by  2;  by  4;  by  6;  by  8;  by  7;  by  10. 

18.  Multiply  5,  4,  7,  6,  9,  10,  8,  3,  5,  7,  6,  9,  2,  5,  8, 
3, 11,  9,  12, 

by  3;  by  5;  by  7;  by  10;  by  4;  by  8. 

19.  Multiply  6,  5,  8,  9,  7,  5,  4,  3,  8,  7,  9, 10,  12,  6,  8, 

9,  11,  2,  5, 

by  4;  by  3;  by  5  ;  by  7  ;  by  6  ;  by  12. 

20.  Multiply  8,  7,  5,  6,  12,  4,  9,  10,  4,  6,  8,  7,  11,  10, 
9,  8,  2,  3,  5, 

by  5;  by  4;  by  6;  by  8  ;  by  3  ;  by  11. 

21.  Multiply  7,  8,  9,  5,  4,  8,  3,  4,  6,  5,  10,  3,  8,  2,  6, 
4,  9,  11, 12, 

by  6  ;  by  5  ;  by  7  ;  by  9  ;  by  4  ;  by  3. 

22.  Multiply  5,  4,  3,  2,  5,  9,  7,  8,  6,  7,  6,  8,  9,  10,  5, 

4. 11,  12,  7, 

by  7  ;  by  4  ;  by  3  ;  by  8  ;  by  9  ;  by  10. 

23.  Multiply  4,  3,  5,  8,  6,  7,  9,  8,  2,  5,  10,  9,  3,  7,  6, 

5. 12,  11,  9, 

by  8;  by  2;  by  3  ;  by  7  ;  by  4  ;  by  6. 

24.  Multiply  12,  7,  6,  8,  5,  4,  9,  8,  7,  6,  5,  9,  3,  10, 
11,  8,  9,  6,  5, 

by  9;  by  3;  by  6;  by  5  ;  by  7  ;  by  12. 


30  MULTIPLICATION 

11.  1.  At  20  cents  a  yard,  how  much  will  7  yards  of 
ribbon  cost  ? 

Solution:  —  Since  1  yard  of  ribbon  costs  20  cents,  7  yards  will 
cost  7  times  20  cents  or  140  cents.  Therefore  7  yards  will  cost  140 
cents. 

2.  At  the  rate  of  30  miles  per  hour,  how  far  will  a 
train  go  in  8  hours? 

3.  A  man  smokes  2  cigars  per  day  at  10  cents  each. 
How  much  will  his  cigars  cost  in  30  days  ? 

4.  My  watch  cost  10  times  as  much  as  my  coat,  for 
which  I  paid  $20.     How  much  did  my  watch  cost? 

5.  If  a  mechanic  earns  $3  per  day,  how  much  does 
he  earn  in  30  days? 

6.  At  the  rate  of  12  miles  per  hour,  how  far  can 
a  steamer  go  in  40  hours  ? 

7.  How  much  must  be  paid  for  8  pounds  of  coffee, 
at  30  cents  per  pound? 

8.  If  9  men  can  do  a  piece  of  work  in  40  days,  how 
long  will  it  take  one  man  to  do  it  ? 

9.  A  cubic  foot  of  lead  weighs  11  thousand  ounces. 
How  many  thousand  ounces  do  12  cubic  feet  of  lead 
weigh  ? 

10.  A  man  worked  9  months  at  180  per  month. 
How  much  should  he  receive? 

11.  If  I  can  save  $  20  per  month,  how  much  can  I 
save  in  a  year  ? 

12.  A  drover  sold  80  cattle  at  $60  each.  How  much 
did  he  get  for  them  ? 

13.  What  will  be  the  cost  of  8  horses  at  $120  each? 

14.  A  man  works  10  hours  per  day  for  30  days. 
How  many  hours  does  he  work  ? 


MULTIPLICATION  31 

15.  There  are  60  minutes  in  one  hour.     How  many 
minutes  are  there  in  9  hours  ? 

16.  At  90   cents   per   bushel,  how  much  will   120 
bushels  of  potatoes  cost  ? 

17.  At  8  cents  a  quart,  how  much  will  20  quarts  of 
berries  cost  ? 

18.  How  many  horses  will  consume  as  many  bushels 
of  oats  in  one  day  as  7  horses  will  consume  in  11  days  ? 

19.  If  a  boy  can  ride  a  bicycle  10  miles  in  one  hour, 
how  far  can  he  ride  in  16  hours  ? 

20.  There  are  12  inches  in  one  foot.      How  many 
inches  are  there  in  9  feet  ? 

21.  What  will  be  the  cost  of  30  pounds  of  beef,  if 
one  pound  costs  11  cents  ? 

22.  In  an  orchard  there  are  11  trees  in  a  row  and  9 
rows.     How  many  trees  are  there  in  the  orchard  ? 

23.  James  has  25  postage  stamps  and  John  has  5 
times  as  many.     How  many  has  John  ? 

24.  A  newsboy  sold  25  papers  at  3  cents  each.     How 
much  did  he  receive  for  them  ? 

25.  A   boy  works   7  examples  a  day.     How  many 
does  he  work  in  80  days  ? 

26.  How  many  ounces  of  candy  are  there  in  8  boxes, 
each  containing  2  pounds  and  a  half,  or  40  ounces  ? 

27.  If  9  firecrackers  are  sold  for  one  cent,  how  many 
can  a  boy  get  for  30  cents  ? 

28.  How  much   money  will  a  street-car  conductor 
collect  from  25  passengers,  if  the  fare  is  5  cents  ? 


32  MULTIPLICATION 

12.  1.  How  much  must  be  paid  for  two  boxes  of 
oranges,  each  containing  200  oranges,  at  2  cents  each? 

2.  How  much  can  a  man  earn  in  30  days,  working  9 
hours  a  day,  at  20  cents  an  hour? 

3.  How  much  is  3  times  8  times  5  ?  9  times  6  times 
10?  4  times  5  times  6?  5  times  12  times  6? 

4.  How  much  is  7  times  8  times  10  ?  4  times  12  times 
10?  20  times  30  times  10?  30  times  40  times  20? 

5.  I  bought  5  bags  of  coffee,  each  containing  60 
pounds,  at  20  cents  a  pound.  How  much  did  the  coffee 
cost? 

6.  How  much  will  the  glass  for  12  windows  cost  at 
10  cents  a  pane,  if  there  are  8  panes  in  each  window? 

7.  How  much  will  120  square  yards  of  plastering 
cost  at  30  cents  a  square  yard? 

8.  Two  mahogany  boards,  each  containing  28  square 
feet,  are  sold  for  10  cents  a  square  foot.  How  much  is 
received  for  them  ? 

9.  How  much  will  be  received  for  9  barrels  of  sirup, 
each  containing  40  gallons,  if  it  is  retailed  at  50  cents  a 
gallon  ? 

10.  I  bought  20  dozen  pairs  of  shoes  at  $  2  a  pair. 
How  much  did  they  all  cost? 

11.  A  dairyman  has  60  cows  that  give  a  daily 
average  of  12  quarts  of  milk  each.  He  sells  the  milk 
at  6  cents  a  quart.  How  much  does  he  get  for  it  in 
10  days? 

12.  In  720  revolutions  of  a  28-inch  wheel,  a  bicycle 
goes  a  mile.  How  many  revolutions  will  it  make  in 
going  20  miles? 


MULTIPLICATION  33 

13.  How  much  will  it  cost  to  put  down  600  square 
feet  of  sidewalk  at  30  cents  per  square  foot? 

14.  How  much  will  25  chickens  cost  at  50  cents 
apiece  ? 

15.  How  much  will  20  tons  of  hay  cost  at  $17  per 
ton? 

16.  How  much  will  30  cows  cost  at  $29  per  head  ? 

13.  1.  What  will  be  the  cost  of  5  oranges  at  3  cents 
apiece  and  6  apples  at  2  cents  apiece  ? 

Solution  :  —  They  will  cost  the  sum  of  5  times  3  cents  and  6 
times  2  cents.  5  times  3  cents  are  15  cents,  and  6  times  2  cents 
are  12  cents ;  15  cents  and  12  cents  are  27  cents.     Therefore,  etc. 

2.  Find  the  cost  of  5  pounds  of  sugar  at  6  cents  a 
pound,  and  3  quarts  of  berries  at  8  cents  a  quart. 

3.  How  much  must  be  paid  for  3  pounds  of  rice  at  6 
cents  a  pound,  and  4  quarts  of  beans  at  8  cents  a  quart  ? 

4.  I  bought  2  loaves  of  bread  at  8  cents  a  loaf,  and 
4  quarts  of  milk  at  7  cents  a  quart.  How  much  did 
they  cost? 

5.  A  man  rides  5  hours  in  a  carriage  at  the  rate  of  9 
miles  an  hour,  and  walks  8  hours  at  the  rate  of  3  miles 
an  hour.     How  far  does  he  go? 

6.  How  much  change  should  I  receive  out  of  50 
cents  after  paying  for  4  pounds  of  beef  at  9  cents  a 
pound,  and  two  cabbages  at  6  cents  per  head  ? 

7.  A  man  has  80  miles  to  go,  and  drives  8  hours  at 
7  miles  per  hour.     How  far  has  he  yet  to  go  ? 

8.  At  2  cents  apiece,  how  much  will  5  dozen  eggs 
cost  ? 

MILNE    MENTAL  —  3 


34  MULTIPLICATION 

9.  At  $6  a  ton,  what  will  be  the  cost  of  enough  coal 
to  last  8  months,  if  2  tons  last  one  month  ? 

10.  What  will  be  the  cost  of  8  yards  of  ribbon  at  9 
cents  a  yard,  and  4  yards  of  calico  at  7  cents  a  yard? 

11.  John  earns  $15  per  week  and  pays  $6  per  week 
for  his  board.     How  much  does  he  save  in  20  weeks  ? 

12.  A  and  B  travel  in  opposite  directions  from  the 
same  point,  at  the  rate  of  6  miles  and  9  miles  per  hour 
respectively.     How  far  apart  will  they  be  in  8  hours  ? 

13.  Two  brothers  who  receive  $20  per  week  each, 
expend  weekly  $12  and  $9  respectively.  How  much 
do  they  together  save  in  10  weeks? 

14.  A  three-story  house  has  two  flights  of  stairs  of 
15  and  14  steps  respectively.  How  many  steps  must  a 
person  take  in  going  up  and  down  5  times? 

15.  A  music  teacher  gives  8  lessons  per  day  at  $2 
per  lesson.     How  much  does  he  earn  in  6  days? 

16.  A  farmer  takes  to  a  mill  9  loads  of  wheat  of  40 
bushels  each,  and  4  loads  of  50  bushels  each.  How 
much  is  it  worth  at  1 1  per  bushel  ? 

14.  1.  What  is  the  cost  of  5  tons  of  hay  at  $18  a 
ton  ? 

2.  A  man  traveled  34  miles  per  day  for  5  days,  and 
had  30  miles  still  to  travel.  What  was  the  length  of 
the  journey? 

3.  How  much  must  be  paid  for  2  dozen  shirts  at  75 
cents  apiece  ? 

4.  A  grocer  sold  30  pounds  of  dried  beef  at  18 
cents  a  pound.     How  much  did  he  get  for  it  ? 


MULTIPLICATION  35 

5.  What  is  the  cost  of  9  cows  at  $37  each  ? 

6.  How  many  words  are  there  on  a  page  of  32  lines 
that  average  12  words  to  a  line  ? 

7.  How  many  times  15  are  8  times  15  and  4  times 
15? 

8.  I  bought  at  one  time  12  pounds  of  meat  at  20 
cents  a  pound  and  at  another  time  18  pounds  at  the 
same  price.     How  much  did  both  quantities  cost  ? 

9.  At  18  cents  per  pound,  how  much  more  must  be 
paid  for  21  pounds  of  butter  than  for  12  pounds  ? 

10.  Find  the  sum  of  13  times  48  and  17  times  48. 

Suggestion  :  — 13  times  48  added  to  17  times  48  equals  30  times 

48. 

11.  A  man  drives  for  three  days  at  the  rate  of  8 
miles  per  hour.  The  first  day  he  drives  7  hours,  the 
second  11,  and  the  third  12.  How  far  does  he  drive 
in  all  ? 

12.  From  one  hive  a  man  got  35  pounds  of  honey, 
and  from  another  45  pounds.  He  sold  it  all  at  25  cents 
a  pound.     How  much  did  he  get  for  it  ?     , 

13.  One  cask  contains  98  gallons  of  vinegar,  and 
another  53  gallons.  It  is  sold  for  60  cents  a  gallon. 
How  much  more  is  received  for  the  first  cask  than  for 
the  second? 

14.  How  much  water  will  supply  a  house  for  one 
week,  if  250  gallons  are  used  daily  ? 

15.  A  woman  sold  to  a  grocer  5  dozen  eggs  at  one 
time  and  7  dozen  at  another,  at  25  cents  a  dozen.  She 
received  in  payment  6  pounds  of  tea  worth  40  cents  a 
pound.     How  much  was  still  due  her  ? 


DIVISION 


15.  1.  How  many  oranges  at  3  cents  each  can  be 
bought  for  24  cents  ? 

Solution  :  —  Since  the  oranges  cost  3  cents  apiece,  as  many  can 
be  bought  for  24  cents  as  3  cents  are  contained  times  in  24  cents, 
or  8  oranges.  • 

Therefore,  at  3  cents  apiece,  8  oranges  can  be  bought  for  24  cents. 

2.  At  5  cents  a  pound,  how  many  pounds  of  sugar 
can  be  bought  for  25  cents  ? 

3.  If  28  cents  are  divided  equally  among  4  boys,  how 
much  will  each  receive  ? 

Solution:  —  Since  the  money  is  to  be  divided  equally  among 
4  boys,  each  will  receive  one  of  the  four  equal  parts  of  it,  or  one 
fourth  of  it.     One  fourth  of  28  cents  is  7  cents. 

Therefore  if  28  cents  are  divided  equally  among  4  boys,  each 
boy  will  receive  7  cents. 

4.  If  5  men  consume  35  ounces  of  bread  per  day, 
how  much  is  that  for  each  man  ? 

5.  When  coal  is  $4  per  ton,  how  many  tons  can  be 
bought  for  1 36? 

6.  A  dealer  bought  flour  for  $  72,  at  $  8  per  barrel. 
How  many  barrels  were  purchased  ? 

7.  If  45  acres  are  divided  into  9  equal  lots,  how 
many  acres  are  there  in  each  lot  ? 


DIVISION  37 

8.  If  $  63  is  paid  for  7  tons  of  hay,  what  is  the  price 
per  ton  ? 

9.  In  8  hours  a  man  rode  72  miles  on  a  bicycle. 
What  was  his  rate  per  hour  ? 

10.  How  many  pounds  of  meat  at  12  cents  a  pound 
can  be  bought  for  $  1.20  ? 

11.  Divide   54   nuts  equally  among  6  boys.     How 
many  does  each  receive  ? 

12.  If  12  pounds  of  rice  cost  84  cents,  how  much  did 
it  cost  per  pound  ? 

13.  In  9  feet  there  are  108  inches ;  how  many  inches 
are  there  in  1  foot  ? 

14.  A  man  drives  64  miles  in  8  hours.     What  is  his 
rate  per  hour  ? 

15.  At  12  cents  a  dozen,  how  many  dozen  eggs  can 
be  bought  for  $1.32? 

16.  A  drover  sold  6  sheep  for  $42.     How  much  did 
they  bring  per  head  ? 

17.  Mary  paid  45  cents  for  some  ribbon  at  9  cents 
per  yard.     How  many  yards  did  she  buy  ? 

16.   1.    If  3  books  cost  $1.20,  how  much  do  they  cost 
apiece  ? 

2.  I  paid  $4  for  20  pounds  of  butter.     How  much 
did  I  pay  per  pound  ? 

3.  When  $3.20  will  pay  for  80  pounds  of  brown 
sugar,  how  much  is  it  per  pound  ? 

4.  How  much   are    oranges   apiece,  when  50   cost 

$2.50? 


38  DIVISION 

5.  A  grocer  paid  $6  for  30  dozen  eggs.     How  much 
did  they  cost  him  per  dozen  ? 

Suggestion:  —  $6  is  equal  to  600  cents. 

6.  A  farm  of  200  acres  is  bought  for  $6000.    What 
is  the  price  per  acre  ? 

7.  If  40  horses  cost  $8000,  what  was  the  average 
cost  per  head  ? 

8.  If  the  weight  of  20  sacks  of  coal  is  4000  pounds, 
how  much  does  one  sack  weigh  ? 

9.  If  10  tons  of  hay  cost  $98,  what  is  the  cost  of 
one  ton  ? 

10.  At  8  cents  a  pound,  how  many  pounds  of  rice 
can  be  bought  for  $16  ? 

11.  If  8  men  earn  $  96  in  4  days,  how  much  does  each 
man  earn  per  day  ? 

Suggestion  :  —  Each  man  earns  $  12  in  4  days. 

12.  If  2  eggs  are  bought  for  5  cents,  how  many  can 
be  bought  for  $1? 

Suggestion:  —  As  many  times  2  eggs  as  5  cents  is  contained 
times  in  $  1. 

13.  In  12  class  rooms  there  are  600  desks.  If  each 
room  contains  the  same  number,  how  many  are  there 
in  each  room  ? 

14.  When  coal  is  $5.50  a  ton,  how  many  tons  can  be 
bought  for  $550? 

15.  How  many  yards  of  muslin  at  5  cents  a  yard 
can  be  bought  for  $8? 

16.  How  much  were  shoes  a  pair  when  40  pairs  cost 
$100? 

17.  At  30  cents  per  pound,  how  many  pounds  of 
coffee  can  be  bought  for  $15? 


DIVISION  39 

17.  1.  Mary  buys  9  yards  of  ribbon  at  12  cents  a 
yard  and  receives  17  cents  change.  How  much  money 
does  she  give  the  merchant  ? 

2.  When  pears  were  8  cents  each,  a  boy  gave  75 
cents  for  5  pears  and  7  peaches.  How  much  did  he 
pay  apiece  for  the  peaches? 

3.  If  8  quarts  of  berries  worth  10  cents  a  quart 
are  exchanged  for  5  yards  of  ribbon  and  15  cents  in 
money,  how  much  is  the  ribbon  worth  per  yard  ? 

4.  If  4  chickens  at  30  cents  each  and  5  ducks  cost 
together  $  3,  how  much  do  the  ducks  cost  apiece  ? 

5.  A  and  B  had  each  50  acres  of  land.  After  A 
had  sold  B  23  acres  and  had  bought  back  31  acres, 
how  many  acres  had  each  ? 

6.  A  cistern  holding  500  gallons  is  full.  After  two 
pipes  have  been  open  8  hours,  one  of  which  carries  away 
200  gallons  an  hour,  and  the  other  brings  in  150  gallons 
an  hour,  how  much  remains  in  the  cistern  ? 

7.  If  20  bushels  of  wheat  will  make  5  barrels  of 
flour,  worth  $  8  a  barrel,  what  is  the  value  of  the  flour 
made  from  one  bushel  of  wheat  ? 

8.  A  man  bought  24  sheep  for  $60  and  sold  them 
so  as  to  gain  $36.  How  much  did  he  get  for  them  per 
head  ? 

9.  A  grocer  buys  a  kit  of  mackerel  for  $5.  If  there 
are  50  mackerel  in  the  kit,  and  he  sells  them  at  the 
rate  of  2  for  25  cents,  what  is  his  gain  ? 

10.  If  5  bushels  of  oats  cost  as  much  as  4  bushels 
of  rye,  and  4  bushels  of  rye  are  worth  3  bushels  of 
wheat,  how  much  must  be  paid  for  oats  when  wheat  is 
$1  a  bushel? 


40  DIVISION 

11.  I  buy  chickens  at  the  rate  of  8  for  $3  and  sell 
them  at  the  rate  of  8  for  $5.  If  my  gain  is  $100, 
how  many  do  I  sell  ? 

12.  Four  men  agree  to  build  a  wall  in  8  days  for 
$120.  After  they  have  worked  4  days,  two  more  men 
are  engaged.  How  much  should  each  receive  if  the 
work  is  finished  in  the  time? 

13.  A  grocer  makes  a  mixture  of  5  pounds  of  tea 
worth  40  cents  a  pound,  and  3  pounds  worth  60  cents 
a  pound  and  sells  it  all  so  as  to  gain  $1.  How  much 
does  he  get  for  it  per  pound  ? 

14.  A  baker  buys  20  tons  of  coal  in  three  months. 
How  much  does  he  pay  for  coal  in  a  year,  if  it  costs  $6 
per  ton  ? 

15.  How  many  men  will  be  required  to  do  as  much 
work  in  3  days  as  7  men  can  do  in  9  days  ? 

16.  What  will  be  the  cost  of  11  yards  of  ribbon,  if 
4  yards  cost  $  1  ? 

17.  A  girl  expended  $  3  for  dress  goods,  at  the  rate 
of  2  yards  for  75  cents.  How  many  yards  did  she 
buy? 

Suggestion  :  —  She  bought  as  many  times  2  yards  as  75  cents  is 
contained  times  in  $3. 

18.  How  many  pounds  of  beef  at  18  cents  a  pound 
should  be  exchanged  for  9  dozen  eggs  at  14  cents  a 
dozen  ? 

19.  A  quantity  of  provisions  will  last  9  men  18 
days.     How  long  will  it  last  6  men? 

20.  If  50  yards  of  cloth  at  90  cents  a  yard  are  ex- 
changed for  flour  at  $5  per  barrel,  how  many  barrels 
will  be  received? 


DIVISION  41 

21.  If  a  man  can  drive  37  miles  in  5  hours,  how  far 
can  he  drive  in  25  hours  ? 

22.  If  the  current  of  a  river  runs  3  miles  per  hour, 
how  far  can  a  man  go  in  10  hours  down  and  10  hours 
up  stream,  his  rate  of  rowing  in  still  water  being  6 
miles  per  hour  ? 

Suggestion  :  —  The  current  aids  him  3  miles  per  hour  going 
down  stream  and  retards  his  progress  3  miles  per  hour  in  going  up. 

23.  I  sold  5  houses  at  $300  each,  and  invested  the 
money  in  lots  at  $  50  each.     How  many  lots  did  I  buy  ? 

24.  A  had  20  sheep ;  B  had  twice  as  many.  They 
were  all  sold  for  $300.  What  was  the  selling  price 
per  head  ? 

25.  I  bought  some  hay  for  $100.  After  using  2 
tons  I  sold  the  remainder  at  $15  a  ton,  and  received 
$  20  more  than  I  paid  for  all  of  it.  How  many  tons 
did  I  buy  ? 

26.  A  man  sold  a  house  for  $9000.  He  invested 
the  proceeds  in  lots  at  $200  each  and  sold  them  at 
$  250  each.     How  much  did  he  gain  ? 

27.  A  dairyman  buys  milk  at  5  cents  a  quart  and 
sells  it  at  8  cents  a  quart.  His  profits  are  $  36  per  week. 
How  much  does  he  sell  per  week  ? 

28.  A  and  B  travel  3  miles  and  5  miles  per  hour 
respectively.  At  the  end  of  a  certain  time  they  are 
240  miles  apart.  How  long  has  each  traveled,  if  they 
started  at  the  same  time  from  the  same  point  and  went 
in  opposite  directions? 

29.  If  7  sheep  are  worth  $  29,  how  many  sheep  are 
worth  $  580  ? 

Suggestion:  —  1 580  is  20  times  $29,  therefore  the  number  of 
sheep  is  20  times  7. 


42  DIVISION 

30.  How  many  apples  can  be  bought  for  69  cents 
if  11  apples  cost  23  cents? 

31.  If  3  pounds  of  fish  cost  the  same  amount  as  2 
pounds  of  beef,  how  much  must  be  paid  for  5  pounds  of 
beef  when  fish  is  12  cents  a  pound  ? 

32.  John  can  earn  as  much  in  3  days  as  his  sister 
can  in  5  days.  How  much  should  John  get  per  day 
when  his  sister  is  paid  75  cents  per  day  ? 

33.  A  man  gave  50  cents  and  his  wages  for  3  days 
for  a  pair  of  shoes  at  82.75  and  5  yards  of  cloth  at  75 
cents  per  yard.     What  were  his  wages  per  day? 

34.  Two  hogs  weigh  together  480  pounds,  and  one 
of  them  weighs  twice  as  much  as  the  other.  What 
does  each  weigh? 

Suggestion  :  —  Three  times  the  weight  of  the  smaller  is  480 
pounds. 

35.  If  2  thousand  feet  of  lumber  cost  $  42,  how  much 
will  9  thousand  feet  cost? 

36.  If  a  man  can  drive  9  miles  an  hour  and  walk  3 
miles  an  hour,  how  long  will  it  take  him  to  drive  to  a 
place  45  miles  away  and  walk  back  ? 

37.  A  has  15  sheep;  B  has  twice  as  many  less  6. 
They  are  all  sold  for  $195.     How  much  is  that  apiece? 

38.  If  I  had  $  15  more  I  could  buy  12  sheep  at  15  a 
head,  but  I  expend  my  money  for  hay  at  $  9  a  ton. 
How  much  hay  do  I  buy  ? 

39.  A  cistern  filled  with  100  gallons  of  water  has  a 
pipe  that  can  empty  it  in  5  hours  and  another  that,  sup- 
plies water  at  the  rate  of  15  gallons  an  hour.  If  both 
pipes  are  opened,  how  soon  will  the  cistern  be  emptied  ? 


DIVISION  43 

40.  If  an  acre  of  ground  will  make  17  city  lots,  for 
how  much  apiece  must  the  lots  be  sold  to  gain  $1400 
on  an  acre  bought  for  $2000? 

41.  A  man  exchanged  9  horses  worth  $200  apiece 
and  a  house  worth  $1200,  for  10  acres  of  land.  How 
much  did  the  land  cost  him  per  acre? 

42.  My  butcher  took  back  a  ham  weighing  12  pounds 
which  he  had  sold  me  at  20  cents  a  pound,  and  gave 
me  in  exchange  for  the  ham  and  60  cents,  a  turkey 
weighing  20  pounds.  How  much  per  pound  did  the 
turkey  cost  me? 

43.  A  grocer  made  a  mixture  consisting  of  8  pounds 
of  coffee  that  cost  him  30  cents  a  pound,  and  4  pounds 
that  cost  him  20  cents  a  pound.  He  sold  the  mixture 
so  as  to  gain  40  cents.  What  was  the  selling  price  per 
pound? 

44.  A  bought  a  horse  for  $100  and  sold  it  to  B  for 
$150.  Later  he  bought  it  back  for  $125  and  sold  it 
again  so  as  to  gain  $40  on  the  entire  transaction. 
What  was  the  last  selling  price  of  the  horse? 

45.  John  takes  5  steps  while  his  father  takes  3. 
How  many  will  each  have  taken  when  together  they 
have  taken  160  steps  ? 

46.  What  I  owed  A  is  3  times  what  I  owed  B. 
After  I  had  paid  both  I  had  $  20  left  out  of  a  one-hun- 
dred-dollar  bill.     How  much  did  I  owe  each  ? 

47.  If  a  man  receives  40  pounds  of  sugar  in  exchange 
for  25  pounds  of  cheese  at  8  cents  per  pound,  what  is 
the  price  of  the  sugar  per  pound  ? 


FRACTIONS 


18.   1.    How  many  halves  are  there  in  1  apple?  in 
2  apples? 

2.  How  many  halves  are  there  in  3  ?  in  5  ?  in  4  ? 

3.  How  many  halves  are  there  in  6?  in  9?  in  8? 

4.  A  boy  cut  three  apples  into  halves.     How  many 
halves  were  there? 

5.  If  a  half  ton  of  coal  costs  $  3,  how  much  will  one 
ton  cost?  4  tons? 

6.  If  a  half  yard  of  silk  is  worth  $2,  how  much  is 
one  yard  worth  ?  3  yards  ? 

7.  How  many  ones  are  there  in  10  halves?  in  16 
halves  ?  in  20  halves  ?  in  18  halves  ?  in  36  halves  ? 

8.  How  many  ones  are  there  in  12  halves?  in  14 
halves  ?  in  24  halves  ?  in  22  halves  ?  in  40  halves  ? 

9.  What  is  a  half  of  2?  of  4?  of  8?  of  12? 

10.  What  is  a  half  of  6  ?  of  10  ?  of  20?  of  16  ? 

11.  If  6  is  half  of  a  number,  what  is  the  number? 

12.  How  many  halves  are  there  in  2  and  1  half  ? 
Solution  :  —  Since  in  1  there  are  2  halves,  in  2  there  are  2  times 

2  halves,  or  4  halves;  4  halves  and  1  half  are  5  halves. 
Therefore,  in  2  and  1  half  there  are  5  halves. 


FRACTIONS  45 

13.  How  many  halves  are  there  in  3^?  in  5J?  in  8J? 

14.  How  many  halves  are  there  in  4^?  in  7|  ?  in  10£  ? 

15.  How  many  ones  are  there  in  11  halves? 

Solution:  —  Since  2  halves  =  one,  11  halves  =  as  many  ones  as 
there  are  2's  in  11,  or  5^. 
Therefore,  11  halves  =  5£. 

16.  How  many  ones  are  there  in  J^-?  in  |?  in  ty? 

17.  How  many  ones  are  there  in  J^-?  in  ^-?  in  V? 

18.  What  is  a  half  of  7?  of  9?  of  15?  of  21  ? 

19.  1.    How  many  thirds  are  there  in  1?  in  3?  in  5? 
in  7  ?  in  8  ?  in  11  ?  in  13  ?  in  30  ? 

2.  How  many  thirds  are  there  in  4?  in  10?  in  6? 
in  12?  in  9  ?  in  15  ?  in  18  ?  in  25  ? 

3.  If  J  of  a  pie  is  worth  5  cents,  how  much  is  a 
whole  pie  worth?     How  much  are  2  pies  worth? 

4.  If  -J-  of  a  melon  costs  10  cents,  how  much  will  2 
melons  cost? 

5.  How  many  ones  are  there  in  |-?  in  *£•?  in  -^-? 
in  JJL?  in  -2/?  in  ^  ?  in  48  ?  in  4f  ? 

6.  How  many  ones  are  there  in  ^  ?  m  |?  in  ^? 
in  2±?  in  JL8_  ?  in  M-?  in  42  ?  in  iLL  ? 

7.  How  many  thirds  are  there  in  1^-?  in  2|?  in  3J? 
in  5§?  in  6f  ?  in  5£?  in  8£?  in  7|? 

8.  How  many  thirds  are  there  in  4|?  in  7J?  in  3|? 
in  101?  in8f  ?  in6i?  in  9|  ?  in  llf  ? 

9.  How  many  ones  are  there  in  -£?  in  ^?  in^-? 
in  3£ ?  in  -2/  ?  in  ^  ?  in  J^  ?  in  ^  ? 

10.    How  many  ones  are  there  in  -^  ?  in  J^-?  in  -^-? 
in  *&  ?  in  %&-  ?  in  ^  ?  in  ^  ?  in  ^  ? 


46  FRACTIONS 

11.  If  §  of  a  melon  is  worth  20  cents,  how  mnch  is 
£  of  the  melon  worth  ? 

12.  A  man  pays  $  60  for  f  of  an  acre  of  land.  How 
much  does  he  pay  for  ^  of  an  acre  ? 

13.  If  a  man  can  walk  4  miles  in  1^  hours,  how  far 
can  he  walk  in  £  of  an  hour  ?  in  1  hour  ?  in  4  hours  ? 

Suggestion:  —  1J  hours  should  be  considered  as  f  of  an  hour. 

14.  For  If  yards  of  ribbon,  Mary  pays  15  cents. 
How  much  does  she  pay  for  £  of  a  yard?  How  much 
for  a  yard? 

15.  If  If  watermelons  cost  40  cents,  how  much  does 
J  of  a  watermelon  cost?  How  much  does  one  water- 
melon cost? 

16.  A  man  can  do  f  of  a  piece  of  work  in  5  days. 
In  how  many  days  can  he  do  the  entire  work  ? 

17.  How  long  does  1  ton  of  coal  last  if  3  tons  last 
one  month? 

18.  When  3f  acres  of  land  cost  $440,  what  is  the  cost 
of  f  of  an  acre  ?  of  1  acre  ? 

19.  If  |  of  my  money  is  $  20,  what  is  f  of  my  money  ? 
How  much  money  have  I  ? 

20.  For  If  weeks'  work  I  pay  $16.  How  much  do 
I  pay  for  |of  a  week's  work  ?  how  much  for  a  week's 
work? 

21.  If  If  cords  of  wood  cost  $10,  how  much  does 
f  of  a  cord  cost?     How  much  does  one  cord  cost? 

20.  1.  How  many  fourths  are  there  in  1?  in  3? 
in  5?  in  7?  in  10?  in  12?  in  14? 

2.    How  many  fourths  are  there  in  4  ?  in  8  ?  in  6  ? 


FRACTIONS  47 

3.    How  many  ones  are  there  in  %?  in  ±£-?  in  J^-? 
4     How  many  ones  are  there  in  -^  ?  in  $£■  ?  in  ^t  ? 

5.  How  many  fourths   are  there    in   1J?    in    3^? 
in  2f  ?  in  4f  ?  in  2|?  in  5f  ?  in  6|? 

6.  Change  5f  to  fourths ;  8£;  6f;  12£;  lOf;  9f 

7.  How  many  ones  are  there  in  -^-?  in  -^-?  in  -^-? 

8.  How  many  ones  are  there  in  -^-?  in  %£-!  in  ±£-? 

9.  If  \  of  a  yard  of  ribbon  is  worth  10  cents,  how 
much  is  a  yard  worth  ? 

10.  I  bought  f  of  a  cord  of  wood  for  $6.     What 
was  the  cost  of  \  of  a  cord?  of  one  cord? 

11.  When  1^  pounds  of  mutton  cost  20  cents,  how 
much  does  ^  of  a  pound  cost  ?  one  pound  ? 

Suggestion: — Consider  \\  as  f. 

12.  I  paid  $28  for  1|  tons  of  hay.    How  much  did  \ 
of  a  ton  cost  me  ?     How  much  did  1  ton  cost  ? 

13.  If  5J  tons  of  coal  cost  $  21,  how  much  did  ^  of  a 
ton  cost  ?     How  much  did  1  ton  cost  ? 

11,  What  is  \  of  8?  of  20?  of  32?  of  40? 

15.  How  much  is  f  of  8?  of  12?  of  28?  of  16? 

16.  How  much  is  \  of  17?  of  23?  of  11?  of  15? 

17.  How  much  is  \  of  7?  of  27?  of  18?  of  29? 

18.  How  much  is  -|  of  7  ? 

Solution  :  —  Since  f  is  equal  to  J  of  3,  f  of  7  is  the  same  as  \ 
!  3  times  7.     3  times  7  = 
Therefore,  f  of  7  =  5J. 

19.  Find  |  of  9;  of  5;  of  11  ;  of  3  ;  of  6  ;  of  7. 

20.  A  man  burned  in  a  single  month  |  of  10  tons  of 
coal.     How  much  did  he  burn? 


48  FRACTIONS 

21.  If  2£  bushels  of  wheat  cost  $2.20,  how  much 
must  be  paid  for  ^  of  a  bushel?  How  much  must  be 
paid  for  one  bushel? 

22.  A  farmer  had  11  tons  of  hay,  and  sold  |  of  it. 
How  many  tons  did  he  sell? 

23.  In  1|  hours  a  boy  rode  14  miles  on  a  bicycle. 
How  far  did  he  ride  in  £  of  an  hour?  How  far  did  he 
ride  in  one  hour? 

24.  A  man  bought  a  cow  for  $  40,  and  sold  it  for  | 
of  what  it  cost.     How  much  did  he  get  for  it  ? 

25.  How  much  is  molasses  per  gallon  when  2^  gallons 
cost  90  cents? 

21.  1.  How  many  fifths  are  there  in  1?  in  2?  in  8? 
in  5?  in  9?  in  13  ?  in  18?  in  10? 

2.  How  many  fifths  are  there  in  7?  in  12?  in  6? 
in  11?  in  6  ?  in  14  ?  in  17  ?  in  19  ? 

3.  How  many  ones  are  there  in  *£■?  in  %£■?  in  *£■? 
in^L?  in-lj£?  in^?  in^?  in^.? 

4.  How  many  ones  are  there  in  -^?  in  -^-?  in  ^-? 
inlfii?     in^-?  in^-?  in^-?  in-^? 

5.  How  many  fifths  are  there  in  1^?  in  4|?  in  2^? 
in  7f  ?  in  11£  ?  in  81  ?  in  7f  ?  in  6|  ? 

6.  How  many  fifths  are  there  in  5f  ?  in  4^?  in  7-|? 
in  lOf  ?  in  8f  ?  in  12|  ?  in  13f  ?  in  15f  ? 

7.  How  many  ones  are  there  in  ^-?  in  -^-?  in  -|?  in 
Jg&?  in  If?  in^?  in-^?  in  ^-?  in^-? 

8.  If  £  of  a  ton  of  hay  is  sold  for  $  3,  for  how  much 
should  a  ton  sell? 


FRACTIONS  49 

9.    A  boy  lost  10  marbles,  which  were  f  of  all  he 
had  at  first.     How  many  had  he  at  first? 

10.  If  |  of  a  number  is  9,  what  is  the  number? 

11.  What  is  |  of  10?  of  20?  of  35?  of  25?  of  15? 
of  60  ?  of  30  ?  of  45  ?  of  55  ?  of  40  ? 

12.  What  is  |  of  11?  of  23?  of  7?  of  19?  of  14? 
of  29?  of  18  ?  of  20  ?  of  30  ?  of  24  ? 


13.  How  much  is  f  of  9?  of  12?  of  15?  of  18? 

14.  What  is  |  of  6?  of  13?  of  8?  of  11?  of  4?  of  12? 

15.  What  is  |  of  8?  of  4?  of  6?  of  7?  of  11? 

16.  How  much  coal  do  I  sell,  if  I  have  9  tons  and 
sell  |  of  it? 

17.  What  must  be  paid  for  -f  of  a  ton  of  hay  at  $15 
a  ton? 

18.  A  man  received  $  30  for  plowing  -|  of  a  field. 
How  much  should  he  get  for  plowing  the  whole  field  ? 

19.  A  watermelon  was  cut  into  5  equal  pieces,  and 
3  of  them  were  sold  for  24  cents.  At  that  rate,  for 
how  much  would  the  whole  melon  sell  ? 

20.  If  f  of  a  farm  is  sold  for  $  2000,  how  much  should 
be  received  for  the  whole  farm  ? 

21.  I  sold  f  of  my  lambs  for  $  60.  At  the  same  rate, 
how  much  should  I  get  for  all  of  them? 

22.  John  had  20  marbles,  and  James  had  f  as  many. 
How  many  had  James? 

23.  A  man  has  60  miles  to  travel.  When  he  has 
gone  |  of  the  distance,  how  far  has  he  traveled  ? 

MILNE    MENTAL — 4 


50  FRACTIONS 

22.   1.    How  much  is  §  of  9?  of  15?  of  30?  of  12?  of 

21  ?  of  27  ?  of  18  ?  of  24  ?  of  33  ?  of  36  ? 

2.  What  is  £  of  8?  of  12?  of  32?  of  28?  of  16?  of 
40?  of  60?  of  100?  of  20 ?  of  24 ?  of  36 ? 

3.  How  much  is  £  of  10?  of  30?  of  40?  of  60?  of 
25?  of  35?  of  15?  of  20?  of  45?  of  55? 

4.  What  is  £  of  18?  of  30?  of  12?  of  60?  of  42? 
of  72?  of  48?  of  24 ?  of  36 ?  of  54  ? 

What  is  the  value  of : 

5.  f  of  24?  of  40?  of  64?  of  56?  of  96? 

6.  f  of  21?  of  35?  of  63?  of  28?  of  70? 

7.  $  of  45?  of  27?  of  72?  of  36?  of  108? 

8.  ^  of  60?  of  36?  of  144?  of  120?  of  72? 

9.  £■  of  66?  of  110?  of  88?  of  121?  of  132? 

10.  $  of  40?  of  70?  of  130?  of  190?  of  210? 

11.  How  much  is  £  of  8?  of  10?  of  11?  of  7?  of  5? 

12.  How  much  is  £  of  7?  of  5?  of  9?  of  3?  of  10? 

13.  Find  %  of  8  ;  of  11 ;  of  6 ;  of  7 ;  of  13 ;  of  21. 

What  is  the  value  of : 

14.  f  of  9?  of  12?  19.  f  of  10?  of  5? 

15.  |  of  6?  of  12?  20.  f  of  20?  of  15? 

16.  jj-ofll?  of  20?  21.  -|of25?of20? 

17.  f  of  12?  of  8?  22.  ^  of  7?  of  21? 

18.  f  of  11  ?  of  13?  23.  £  of  13?  of  100? 

24.    John  worked  8  hours,  and   Henry  |  as  long. 
How  long  did  Henry  work? 


FRACTIONS  51 

25.  I  paid  $  9  for  a  cord  of  wood,  and  §  as  much  for 
a  ton  of  coal.  At  that  rate  find  the  cost  of  10  tons  of 
coal. 

26.  A  watch  cost  $  28  and  a  chain  f  as  much.  How 
much  did  both  cost? 

27.  If  a  man  paid  f  of  $  96  for  4  tons  of  hay,  how 
much  did  one  ton  cost? 

28.  Two  boys  together  caught  56  fishes.  If  one  of 
them  caught  |-  of  the  number,  how  many  did  the  other 
catch  ? 

29.  A  barrel  of  sirup  contained  42  gallons  ;  f  of  it 
was  sold  at  60  cents  a  gallon.  How  much  was  received 
for  what  was  sold  ? 

30.  Mr.  Howard  is  60  years  old,  and  |  of  his  age  is 
3  times  his  son's  age.     How  old  is  his  son  ? 

31.  One  boy  had  |  of  a  quart  of  chestnuts,  and  an- 
other had  -^  of  a  quart.  How  many  chestnuts  had 
both  if  there  were  96  chestnuts  in  a  quart  ? 

32.  Three  boys  had  together  240  marbles.  How 
many  of  them  belonged  to  the  third  boy,  if  the  shares 
of  the  first  and  second  boys  were  respectively  J  and  1 
of  the  whole  number  ? 

33.  A  grocer  sold  ^  of  a  tub  of  butter  to  one  cus- 
tomer and  ^  of  it  to  another  customer.  If  the  tub  con- 
tained  42  pounds  at  first,  how  much  remained? 

34.  A  boy  had  72  cents  and  earned  ^  as  much  as  he 
had.     How  much  had  he  then  ? 

35.  Samuel  rode  in  the  forenoon  36  miles  on  his 
bicycle  and  in  the  afternoon  -|  as  far.  How  far  did 
he  ride  that  day? 


52  FRACTIONS 

36.  A  lady  bought  §  of  a  piece  of  sheeting  contain- 
ing 48  yards,  paying  20  cents  a  yard  for  it.  How 
much  change  should  she  receive  out  of  a  ten -dollar 
bill? 

37.  A  farmer  had  360  bushels  of  wheat.  He  sold 
|  of  it  to  one  man  and  %  of  the  remainder  to  another. 
What  was  the  value  of  what  was  left,  at  50  cents  a 
bushel  ? 

23.   1.    How  many  fourths  are  there  in  J? 

Solution  :  —  Since  there  are  f  in  1,  in  \  there  are  \  of  \  or  }. 
Therefore  there  are  2  fourths  in  £. 

2.  How  many  sixths  are  there  in  £?  in  J?  in  $? 

3.  How  many  fourths  are  there  in  f  ?  in  |?  in  3£? 

4.  How  many  eighths  are  there  in  £?   in  -J?   in  |? 
in  1£?  in  2£?  in  3£?  in  2£?  in  4£? 


if;  2J. 

|;M;if;2£. 


5.  Change  to  tenths  :  \  ;  f  ;  £  ;  £ ; 

6.  Reduce  to  twelfths  :  i£;  J;  £;  $; 

7.  Reduce  to  eighteenths :  f ;  £;  £ ; 

8.  By  what  must  the  terms  of  the  fraction  \  be  mul- 
tiplied to  reduce  the  fraction  to  fourths?  to  tenths? 
to  twelfths  ?  to  eighteenths  ? 

9.  What  is  the  effect  on  the  value  of  a  fraction  of 
multiplying  its  terms  by  the  same  number? 

10.  How  many  twentieths   are   there  in  £?    in  £? 
in^?  inf?  in2J?  in^? 

11.  Reduce  to  twenty-fourths :  J;  J;  |;  \\  |;  -^  ; 

12.  Reduce  £,  £,  i  f ,  f ,  f ,  ^,  -fr  and  ±£  to  thirtieths. 


FRACTIONS  53 

13.  Reduce  f,  ■§,  |,  J-J-,  f,  and  J  to  equivalent  frac- 
tions having  a  common  denominator. 

14.  Change  -f,  f ,  ^,  J,  §,  and  f  to  equivalent  frac- 
tions having  their  least  common  denominator. 

Reduce  to  equivalent  fractions  having  their  least 
common  denominator : 

25.    M,2t,M. 

Ofi        11111 
ZD-     ?'   3'  6'   12'  2* 

97       11     4     JL     5     2 
*  • '      18'   9'   36'   6 '   3 • 

28-  f&f&f 

29-  f  *>&,&,*• 

31        3.    _5_     3  9     1    _J_ 
ol1     4'   11'  T¥'  2'  22* 

32-   t.f&A..**** 

^-     TV  A'    5'  F0'   6'   2* 

34       3     5     7    _3_    JL.    _5 
O*.     f,   6>  fi   16>   12>  2J' 

35.  A  man  owned  J  of  a  mill.  If  he  divided  his 
share  among  his  children,  giving  one  fifteenth  of  the 
mill  to  each,  how  many  children  were  there  ? 

36.  If  |  of  a  melon  is  cut  into  twelfths  and  sold  at 
5  cents  for  each  piece,  how  much  will  be  received  for 
it? 

37.  A  girl  cut  If  yards  of  ribbon  into  pieces  each 
containing  one  ninth  of  a  yard.  How  many  pieces 
were  there  ? 

38.  A  coal  dealer  divided  equally  among  some  poor 
families  1^  tons  of  coal,  giving  to  each  family  one  tenth 
of  a  ton.     How  many  families  were  there  ? 


15. 

i  s.  s.  a 

3'  ¥'  6'  2' 

16. 

2    _o_    I    _5_ 
3'  6'   9'   12- 

17. 

f  *»'*.*• 

18. 

2  0'  TO'  TO'  t* 

19. 

1    13     _3__     1 
t'   32'   16'  ¥' 

20. 

1     1  1     5     JL 
4'  L2->  3'   16* 

21. 

3       9      91     11 

5'  TO'  Z2'  2  0' 

22. 

1193      4 

5'   3'  ^5'    15* 

23. 

If  2^,  },  f . 

24. 

h  ItV  f  H- 

54  FRACTIONS 

24.    1.    How  many  fifths  are  there  in  ^|? 

Solution  :  —  Since  \  =  T3?,  |f  =  as  many  fifths  as  T\  is  contained 
times  in  j§,  which  is  4  times. 

Therefore  there  are  4  fifths  in  \%. 

2.  How  many  halves  are  there  in  $?  in  |?  in  J§£? 
ini$?  inT62?  inf#? 

3.  How  many  thirds  are  there  in  -fa  ?  in  -J£?  in  ^-|  ? 
in  |f?  in  A?  inl£?  in  gf  ? 

4.  How  many  fourths  are  there  in  ^?  in  $?  in  £$? 
in  if?  in  f|?  in  fi? 

5.  Reduce.^,  fft  f$,  |£,  £f,  and  ||  to  fourths. 

6.  To  reduce  ^f  to  fourths,  by  what  do  you  divide 
the  terms  of  the  fraction  ?  To  reduce  f^  to  sixths,  by 
what  do  you  divide  ? 

7.  Express  each  of  the  following  fractions  in  smaller 
or  lower  terms  :  f| ;  ff ;  f£  ;   |f  ;  ff  ;  $f 

8.  Reduce  each  of  the  following  fractions  to  its 
lowest  terms  :  #  ;  J§  ;  f§  ;  ||  ;  #  ;  £f  ;  |f . 

9.  Change  to  their  simplest  form :  -1-|,  ^,  f  f,  ||, 

TOO'  "£0'  "BT'  200'  600* 

10.  I  paid  J!  of  $15  for  a  silk  hat.     How  much  did 
it  cost? 

Suggestion  :  —  Reduce  the  fractions  to  their  lowest  terms  before 
solving  the  problem. 

11.  A  man  received  ||  of  $70  for  his  watch.     How 
much  did  he  get  for  it  ? 

12.  How  much  is  ff  of  57?   f£  of  70?  f}  of  60? 
££  of  100?  |f  of  14?  fl  of  25  ?  }f  of  36? 


FRACTIONS  55 

13.  A  boy  had  48  marbles  and  lost  Jf  of  them ;  he 
then  gained  $4  as  many  as  he  had  left.  How  many 
did  he  then  have  ? 

14.  If  Jf  of  what  was  paid  for  a  farm  was  $6000, 
what  was  the  entire  cost  of  the  farm  ? 

15.  A  farmer  sold  ||  of  his  hay  at  $12  per  ton,  and 
received  for  it  $240.     How  mnch  hay  had  he? 

16.  After  sailing  3000  miles,  a  ship  has  completed 
W  of  her  voyage.     What  is  the  length  of  her  voyage  ? 

17.  Mary's  dress  cost  f  §  as  much  as  her  cloak.  How 
much  did  her  dress  cost  if  she  paid  $  36  for  the  cloak  ? 

18.  In  a  school  registering  66  pupils  ^|  of  them  are 
absent.     How  many  are  present  ? 

19.  In  a  race  between  two  boats,  when  the  winner 
had  gone  120  miles  the  other  boat  had  gone  only  |J  of 
this  distance.     How  far  behind  was  the  second  boat  ? 

20.  How  old  is  John  if  ||  of  60  years  is  3  times  his 
age? 

21.  A  grocer  sells  |f  of  a  pound  of  butter  for  25  cents. 
At  that  rate,  how  much  will  he  get  for  8  pounds  ? 

25.   1.    Change  to  thirds:  3f;  51;  8;  10} ;  4£;  9f. 

2.  Change  to  fourths :  8| ;  9£;    12f;  11;  7f;  6f. 

3.  How  many  fifths  are  there  in  6|?  in  5^?  in  8-|? 

4.  In  reducing  8-|  to  fifths,  by  what  is  8  multiplied  ? 
What  is  done  with  the  4  ? 

5.  Reduce  3^  to  an  improper  fraction  ;  5| ;  7-| ;  4-| ; 

H;9fi  ln>1^>  20f;  25f 

6.  Reduce    7|  to  an  improper  fraction ;    8^ ;    10| ; 
12*;  6|;  5f;  8f;  9|;  11*;  lOf 


56  FRACTIONS 

7.  How  many  eighths  are  there  in  lOf  ?  in  6|?  in 
12 J?  in  9|? 

8.  Reduce  to  improper  fractions:  llf ;  5f ;  8|;  6^. 

9.  How  many  ones  are  there  in  J^-?  in  ^-?  in  4^-? 

10.  Change  to  units:  ^5  ¥^  ¥"5  ¥"5  ¥• 

11.  Change  to  units:  Jf ;  2£;  ^;  ^;  ^L. 

12.  Reduce  to  whole  or  mixed  numbers:  %£-;  %g\  ^; 

¥;  ¥;  ¥;  ¥;  ¥?  ¥;  ¥;  ¥• 

13.  Change  to  whole  or  mixed  numbers:  ^;  ^-;  ^; 

¥;  ¥;  ¥;  V;  ¥;  ¥;  ¥;  V- 

14.  Reduce  to  mixed  numbers:  ^-;  -|^;  ^;  ^-;  -^-. 

15.  Reduce  to  mixed  numbers:  ^5^;^;  -V8oa- 

16.  Pies  cut  into  sixths  are  sold  at  5  cents  for  each 
sixth.     How  much  is  received  for  one  dozen  pies  ? 

17.  A  man  plows  a  field  of  5|  acres.  If  he  plows 
one  sixth  of  an  acre  per  hour,  how  long  does  it  take  him 
to  plow  the  field  ? 

18.  Maud  divided  4|  yards  of  ribbon  among  her 
schoolmates,  giving  each  one  ninth  of  a  yard.  How 
many  schoolmates  had  she  ? 

19.  How  far  can  a  man  walk  in  6^  hours  at  the  rate 
of  1  mile  in  15  minutes? 

20.  How  many  more  fifths  than  fourths  are  there  in 
1000? 

21.  A  grocer  bought  40|  gallons  of  vinegar  at  20 
cents  a  gallon,  and  retailed  it  at  10  cents  for  one  fourth 
of  a  gallon.     How  much  did  he  gain? 

22.  How  much  will  be  gained  on  5|  reams  of  paper 
bought  for  $10  and  sold  at  20  cents  a  quire,  there  being 
20  quires  in  a  ream  ? 


FRACTIONS  57 

26.   1.    How  many  halves  are  there  in  J-f-^?     How 
many  units  ? 

2.  How  many  thirds  are  there  in  1  +  §  ?  in  §  +  §  -f  f  ? 
How  many  units  ? 

3.  What  is  the  sum  of  J  and  J?  of  f  and  |  and  ^? 
of  |  and  |  and  f  ?  f  and  f  and  |  ? 

4.  What  is  the  difference  between  f  and  f  ?  f  and 
|?  f.andf?{*ndf?  A«d£? 

5.  How  many  fourths  are  there  in  J  plus  ^  ?  in  f 
plus  J  ?  in  -|  plus  ^  ?  in  |  plus  J-  ? 

6.  How  many  sixths  are  there  in  J  +  J?  in  1  +  1? 

7.  How  many  more  sixths  are  there  in  J  than  in  J? 
in  |-  than  in  J  ?  in  |  than  in  1  ? 

8.  What  is  the  sum  of  l  and  £  ?  -J  and  |?  J  and  J^  ? 

9.  Find  the  sum  of :  J  and  1 ;  J  and  | ;  |  and  -| ; 
f  and  | ;  f  and  TV 

10.    What  is  the  value  of  f-h&?   I +T6?   I  +  f ? 

What  is  the  value  of : 

u-  *+*+*»  17-  *  +  *  +  #?  23.  f+^+|? 

12.  J+f  +  f?  18.    J  +  f  +  A?  24.  f+J  +  tf? 

13-  |  +  |+A?  19-    i  +  f+ft?  25.  f  +  l  +  A? 

14.  i  +  i+^?  20.    t  +  J  +  A?  26.  i  +  f  +  A? 

15-  1  +  KiV?  21.    ^  +  f  +  ^?  27.  J  +  f  +  tf? 

16.  |  +  f+iJ?  22.    i  +  f  +  ^?  28.  *  +  *  +  &? 


58  FRACTIONS 

29.  Mary  bought  £  a  yard  of  ribbon  at  one  time,  and 
|  of  a  yard  at  another  time.  How  much  ribbon  did 
she  buy? 

30.  A  man  had  &  of  an  acre  of  land  and  bought 
another  piece  containing  £  of  an  acre.  How  much  land 
had  he  then? 

31.  What  is  the  sum  of  §  and  f  ? 
Suggestion:  —  §  equals  ^ and  f  equals  jV 

32.  Find  the  sum  of :  J  and  f  ;  J  and  £ ;  £  and  £ ; 
£  and  J ;  J  and  £  ;  §  and  f 

33.  How  much  is  2£  +  3£? 

Solution  :  —  Since  J  =  |,  and  J  =  § ,  the  sum  of  2|  and  3£  is  the 
same  as  the  sum  of  2|  and  3|,  or  5f. 
Therefore  2J  -f-  3J  =  5J. 

34.  Find  the  sum  of  :  1£  +  3£  ;  4|  +  5£  ;  §\  +  b±  + 
4f;  5f  +  7§;  7|  +  8f 

35.  A  lady  at  one  time  bought  2|  yards  of  velvet, 
and  at  another  time  3|  yards.  How  much  did  she  buy 
in  all? 

36.  A  man  walked  3^  miles,  3|  miles,  and  3|  miles 
during  the  first  three  hours  of  a  journey.  How  far  did 
he  walk  in  all  ? 

37.  A  butcher  sent  7J  pounds  of  meat  to  one  cus- 
tomer, and  8|  pounds  to  another.  How  much  did  he 
send  to  both? 

What  is  the  sum  of : 

38.  fandi?      42.    $  and|?  46.  fandf? 

39.  fandi?       43.    fandf?  47.  J,  fa  and  $? 

40.  fandf?       44.    fandf?  48.  f,  f,  andf? 

41.  |  and  §  ?       45.    f  and  J?  49.  T\,'  &,  and  J  ? 


FRACTIONS  59 

50.  £,  &,  and  I?  56.  41  31  and  12£? 

51.  §,  TV  and  |?  57.  7f,  5f,  and  201? 

52.  21  and  3J?  58.  8f,  7|,  and  5^  ? 

53.  4£and5§?  59.  6§,  7f,  and  8f  ? 

54.  7iand4|?  60.  7£,  lOf,  and  9^? 

55.  5fand6§?  61.  5$,  4f,  and  3£? 

62.  A  man  sold  |  of  an  acre  of  land  at  one  time,  and 
|  of  an  acre  at  another  time.     How  much  did  he  sell? 

63.  Jane  studied  her  geography  |  of  an  hour  and 
her  arithmetic  ^  of  an  hour.     How  long  did  she  study  ? 

64.  A  farmer  sold  12f  tons  of  hay  and  kept  10|  tons. 
How  many  tons  had  he  at  first  ? 

65.  Annie  had  45  roses.  She  gave  her  sister  f  of 
them,  and  her  brother  |  of  them.  How  many  had  she 
left? 

66.  If  I  add  together  J,  J,  and  ^  of  a  certain  number, 
the  sum  is  1300.     What  is  the  number  ? 

Suggestion  :  —  ^  +  a  -f  £  of  a  number  is  {§  of  the  number. 
Therefore  if  of  the  number  is  1300. 

67.  My  age  increased  by  its  ^  and  its  -J  is  77  years. 
How  old  am  I  ? 

68.  A  watch  costs  $70,  and  |  of  its  cost  is  twice  the 
cost  of  the  chain.     How  much  does  the  chain  cost  ? 

69.  If  3J  tons  of  coal  are  burned  in  December,  and 
4|  tons  in  January,  how  much  is  burned  in  the  two 
months  ? 

70.  From  a  piece  of  cloth  there  were  cut  at  one  time 
4|  yards,  and  at  another  6|  yards.  If  20^  yards  were 
left,  how  many  yards  were  there  in  the  piece? 


60  FRACTIONS 

27.   1.    What  is  the  difference  between  |  and  J?  | 
and  |?  ^  andf? 

2.  Subtract  J  from  |  ;   \  from  f  ;   |  from  ^  ;   J  from 
\\\   1  from  1£;   J  from  1  J. 

3.  Find  the  value  of  :   |  -  §  ;  11  -  | ;  11  -  |  ;  11 

-  S ;  if  - f ;  it-f 

4.  What  is  the  difference  between  f  and  §?  £  and 
i?£andf?  fandj? 

5.  Subtract  £  from  £ ;  J  from  J  ;  \  from  J  ;   \  from 
£  ;  f  from  §  ;  f  from  f 

6.  What  is  the  value  of  §  -  \  ?  §  -  §?  |  -  i  ?  J  - 

7.  What  is  the  value  of  :  f-f?  |-f?  £--&?  £- 

8.  Subtract  |  from  | ;   |  from  | ;  |  from  § ;  f  from 
| ;  |  from  f ;  f  from  f-. 

Subtract  : 


9. 

1  from  If 

15. 

i  from  If 

21. 

f  from  If 

10. 

f  from  1|. 

16. 

I  ^om  if 

22. 

1  from  ff. 

11. 

§  from  If 

17. 

|  from  |f. 

23. 

|  from  |f 

12. 

|  from  T97. 

18. 

§  from  f 

24. 

4  from  41- 

o                   lb 

13. 

f  from  ff 

19. 

§  from  If 

25. 

f  from  if. 

14. 

1  from  f 

20. 

f  from  If 

26. 

1  from  f 

27. 

A  man  owned  |  of  a  farm  and  sold  \ 

of  the  farm. 

How 

much  did  he  still  own  ? 

28.  Of  a  pole  |-  is  in  the  air,  J  is  in  the  water,  and 
the  remainder  is  in  the  mud.  What  part  of  the  pole 
is  in  the  mud  ? 


FRACTIONS  61 

29.  The  difference  between  J  of  John's  marbles  and 
A  of  them  is  10.     How  many  marbles  has  he  ? 

30.  My  age  10  years  ago  was  equal  to  f  of  my  age 
now.     How  old  am  I  ? 

31.  I  owe  I  of  a  dollar.  How  much  change  should 
I  get  from  f  of  a  dollar  if  I  pay  the  debt  ? 

32.  A  man  bought  ^  of  a  farm  and  sold  J  of  the 
farm.  The  part  of  the  farm  that  he  retained  was  worth 
$2000.     What  was  the  value  of  the  whole  farm  ? 

33.  In  an  orchard  \  of  the  trees  are  peach  trees,  \ 
are  pear  trees,  and  the  rest  are  apple  trees.  What 
part  of  the  trees  are  apple  trees? 

34.  If  A  bought  a  watch  for  J  of  $90,  and  sold  it  for 
|  of  1 90,  how  much  did  he  gain  ? 

35.  A  boy  who  has  48  marbles  loses  §  of  them  and 
then  buys  f  as  many  as  he  had  at  first.  How  many 
has  he  then  ? 

36.  A  paid  $150  for  a  horse  and  |  as  much  for  a 
sleigh.  He  then  sold  them  both  for  -|  of  the  cost  of 
both.     How  much  did  he  lose  ? 

What  is  the  value  of : 


37. 

l  +  h 

-v 

44. 

£  T  12        3  ' 

51. 

t       3^12  • 

38. 

1  4-1 

3+^ 

_1  ? 

6  ' 

45. 

3.__1_4__2    ? 
5       10^1^* 

52. 

6  +  8        12  • 

39. 

l+h 

-|? 

46. 

5._1_±__5_? 
8        3^  12  ' 

53. 

i,_2__l_? 
5       3        15  ' 

40. 

!+!- 

-A? 

47. 

l56+l-i? 

54. 

5  i  j a_? 

8^12        16  • 

41. 

i+h 

_2  ? 
3  ' 

48. 

I-tV+I? 

55. 

i-f  +  T3*? 

42. 

6      ¥^2  ' 

49. 

I+t6o-A? 

56. 

ll  +  3f-lf? 

43. 

5  4.  2  . 

-1? 
9  ' 

50. 

t  +  iWs? 

57. 

4f-2l  +  3f? 

62  FRACTIONS 

58.  9|-4i  +  6£?  63.  8f-5J  +  6A? 

59.  12g  +  5f  —  6f  ?  64.  9§-4&+5$? 

60.  21i+3£-10§?  65.  4J-2f  +  8i? 

61.  81+2^-4^?  66.  8f-4^  +  3i? 

62.  7f  +  56i-3TV?  67.  10|  +  8J-7A? 
68.  Find  the  value  of  5£  -  3|. 

Solution: -5^  =  V;  3!  =  V  5  ¥"=«.  and  ¥=B;  f i  ~  f i 
=  ff  =  l\\.     Therefore  the  value  of  5 J  -  3§  is  Iff.     Or, 

5J  =  5^5  and  3f  =  3^.  Therefore  we  are  to  find  the  difference 
between  5^  and  3T65. 

Since  T\  cannot  be  subtracted  from  T55,  a  unit  or  \%  is  taken 
from  5  and  united  with  fa  making  f  §.  The  minuend  is  now  equal 
to  4fJ,  and  if  3T\  is  subtracted  from  it,  there  is  a  remainder  of  1\%. 
Therefore,  etc. 

Note.  —  It  is  usually  advisable  to  subtract  integers  and  mixed 
numbers  separately. 


Find  the  value  of : 

69.   6J-8J. 

75. 

4|- 

-2|. 

81. 

4A-3J. 

70.   4J-8J. 

76. 

H- 

I* 

82. 

3|-1|. 

71.   8f-2f 

77. 

H- 

-4 

83. 

4i-2f. 

72.   31 -If. 

78. 

3f- 

-n- 

84. 

5J  -  3|. 

73.   5f-l|. 

79. 

H- 

-2f. 

85. 

4f~2fV. 

74.   6£-3£. 

80. 

7|- 

-3|. 

86. 

5|  -  2|. 

28.   1.   What  is  §  of  T^? 

Solution  :  —  ]  of  T%  =  t3q,  and  f  of  T9<y  =  2  times  T%,  or  T%,  equal 
to  f .     Therefore,  etc. 

2.  What  is  f  of  f  ?  of  f  ?  of  if?  of  if?  of  If? 

3.  What  is  f  of  I?  of  I?  of  T\?  of  if?  of  if? 


FRACTIONS  63 

4.  What  is  i  of  f  ?  of  f  ?  of  |?  cf  l£?  of  if? 

5.  What  is  f  of  2i? 

Solution:  —  2\  =  I ;  J  of  f  =  |;  and  }  of  |  =  2  times  |  or  f, 
equal  to  1£.     Therefore,     of  2\  =  1J. 

What  is  the  value  of : 

6.  f  of  11?  of  If?  of  41?  of  2| ?  of  3f? 

7.  |  of  2f  ?  of  If?  of  2|?  of  31?  of  51? 

8.  |  of  If?  of  31?  of  3|?  of  llf?  of  71? 

9.  f  of  4|?  of  10§?  of  9|?  of  6§?  of  4f? 

10.  A  man  had  3|  tons  of  coal  and  burned  f  of  it. 
How  much  did  he  burn  ? 

11.  William  traveled  f  of  6§  miles  per  hour.     What 
was  his  rate  per  hour  ? 

12.  A  dealer  had  17^  bushels  of  corn,  and  sold  f  of 
it.     How  many  bushels  did  he  sell  ? 

13.  A   lady  had  $18|  and  paid  f  of  it  for  a  dress. 
How  much  had  she  left  ? 

14.  If  |  of  $19f  is  what  was  paid  for  a  coat,  how 
much  did  it  cost  ? 

15.  If  |  of  a  plot  of  ground  containing  8  J  acres  is 
sold  for  $  140,  what  is  the  price  per  acre  ? 

16.  What  is  f  off? 

Solution:  —  |  of  f  =  T%,  and  §  of  f  =  2  times  T^,  or  T83.     There- 
fore, etc. 

17.  What  is  f  of  |?  of  i?  of  f?  of  |?  of  |? 

18.  What  is  |  of  |?  of  i?  off?  of  |?  off? 

19.  What  is  |  of  £  ?  of  f?  of  f  ?  of  J?  of  j? 


64  FRACTIONS 

What  is  the  value  of  : 

20.  foff?  23.   f  off?  26.  |  of  If? 

21.  |  off?  24.   |  off?  27.  |  of  2i? 

22.  |  of  J?  25.   foflj?  28.  fof7£? 

29.  A  man  had  12£  tons  of  coal  in  his  cellar.  He 
used  |  of  it  in  his  furnace.     How  many  tons  did  he  use  ? 

30.  If  a  merchant  sells  f  of  a  piece  of  cloth  contain- 
ing 33^  yards  at  60  cents  a  yard,  how  much  does  he  get 
for  it  ? 

31.  A  man  owned  £  of  a  mill  -and  sold  £  of  his  share 
for  $3000.     At  that  rate,  what  was  the  mill  worth  ? 

32.  A  suit  of  clothes  was  sold  for  $25£.  If  it  cost  § 
of  the  selling  price,  how  much  did  it  cost  ? 

33.  A  boat  went  18f  miles  down  the  river.  If  the 
current  carried  it  ^  of  the  distance  and  it  was  rowed 
the  rest  of  the  way,  how  far  was  it  rowed  ? 

34.  A  merchant  bought  £  of  a  stock  of  brooms  and 
sold,  at  the  same  rate,  f  of  what  he  bought.  How 
much  did  he  get  for  them  if  the  whole  stock  was 
worth  $120? 

35.  A  boy  gathered  £  of  a  bushel  of  chestnuts,  and 
sold  |  of  them.  How  much  did  he  get  for  what  he 
sold  if  he  was  paid  at  the  rate  of  $  4.80  per  bushel  ? 

36.  A  grocer  made  a  mixture  of  Mocha  and  Java 
coffee  such  that  -£  of  it  was  Java.  How  many  pounds 
were  there  of  each  if  the  whole  weighed  15|  pounds  ? 

37.  Henry  inherited  f  of  an  estate  valued  at  $  10,000 
and  paid  %  of  his  inheritance  for  20  lots.  How  much 
did  he  pay  for  each  lot  ? 


FRACTIONS  65 

29.  1.  How  much  is  5  times  f  ?  f  ?  f  ?  f  ?  T\?  f? 

2.  How  much  is  4  times  f  ?  £?  §?  f  ?  £?  f  ? 

3.  How  much  is  3  times  f  ?  f  ?  f  ?  ^ ?  ^  ?  T8T? 

4.  What  is  the  difference  between  f  of  4  and  4 
times  J? 

5.  How  much  is  £  of  12?  of  15  ?  of  6?  of  8?  of  20? 

6.  How  much  is  6  times  f  ?  f  ?  £  ?  f  ?  f  ?  f  ?  f  ? 

7.  Multiply  4f  by  5. 

Solution  :  —  5  times  f  =  -1/-,  or  3J ;  5  times  4  =  20 ;  and  20  + 
3}  =  23^.     Therefore  4f  x  5  =  23J. 

8.  Whatisthe  value  of  4^x5?  of6fx4?  of  4|x3? 
of  7f  x  5?  of  6f  x  7?  of  8f  x  8?  of  5£  x  9? 

9.  How  much  is  6  times  4|  ?  7  times  3f  ?  4  times 
5f  ?  8  times  Sf  ?  4  times  9f  ?  5  times  5f  ?  9  times  3f  ? 

10.    How  much  is  5  times  5|  ?  4  times  9^  ?  6  times 
T£?  7  times  7f  ?  8  times  8f  ?  9  times  7|?  6  times  8f  ? 

What  is  the  product  of : 


11. 

4£xl2? 

16. 

8ix7? 

21. 

8x7|? 

12. 

6fxl0? 

17. 

9fx8? 

22. 

9x64? 

13. 

5|x6? 

18. 

7fx6? 

23. 

10x3£? 

14. 

8   x7f? 

19. 

9^x9? 

24. 

12x4£? 

15. 

12fx3? 

20. 

6|   x6? 

25. 

11x3^? 

26.  Irene  bought  8|  yards  of  ribbon  at  12  cents  a 
yard.     How  much  did  it  cost  her  ? 

27.  At  6^  cents  a  pound,  how  much  will  8  pounds 
of  rice  cost? 

28.  When  butter  costs  18-|  cents  a  pound,  how  much 
will  12  pounds  cost? 

MILNE    MENTAL 5 


66  FRACTIONS 

29.  How  far  can  a  man  walk  in  10  hours,  who  goes 
3£  miles  per  hour  ? 

30.  A  man  proposes  to  ride  100  miles.  How  far 
has  he  yet  to  go  after  he  has  ridden  7  hours  at  llf 
miles  per  hour? 

31.  How  much  must  I  pay  for  9|  tons  of  hay  at  $8 
per  ton  ? 

32.  A  farmer  sold  his  apples  in  barrels,  each  con- 
taining 2|  bushels,  at  60  cents  per  bushel.  How  much 
did  he  get  for  them  per  barrel? 

33.  How  much  will  a  farm  of  160  acres  of  wild  land 
cost  at  $  2|  per  acre  ? 

34.  What  will  be  the  cost  of  5|  gallons  of  sirup  at 
60  cents  per  gallon? 

35.  Mary  bought  at  one  time  5§  yards  of  ribbon  and 
at  another  6|  yards.  How  much  did  it  all  cost  her  at 
12  cents  per  yard? 

36.  How  much  change  should  I  receive  out  of  a  five- 
dollar  bill  if  I  pay  for  12  bushels  of  corn  at  $f  per 
bushel? 

37.  Two  men  travel  in  opposite  directions,  one  at  the 
rate  of  3^  miles  an  hour,  and  the  other  at  the  rate  of  4J 
miles  an  hour.     How  far  apart  are  they  in  12  hours? 

38.  I  bought  12  cords  of  hard  wood  at  $  8£  per  cord 
and  5 J  tons  of  coal  at  $5  per  ton.  How  much  did  my 
fuel  cost? 

39.  What  is  the  cost  of  8|  pounds  of  cheese  at  12 
cents  a  pound  and  7£  pounds  of  butter  at  20  cents  a 
pound  ? 


FRACTIONS  67 

30.    1.    How  much  is  3^  times  4§? 

Solution  :  —  3|  =  } ;  4f  =  V4.     I  of  V  =  ¥.  or  |,  and  J  of  V  = 
7  times  J,  or  *f-9  which  is  equal  to  16  £.     Therefore,  etc. 

2.  How  much  is  2*   times  £?     31  times  1J?     8 J 
times  §?     4 1  times  2|? 

3.  What  is  the  product  of  f  x4i?  of  f  x2|?  of  61 
x3|?  of  8ix2f? 

4.  How  much  is  41  times  21?     6£  times  21?     121 
times  11?     7^  times  31? 

What  is  the  value  of : 

5.  7ix6f?       11.    5£x2£?  17.  J  off  of  12? 

6.  4|  xli?      12.    12fx3i?  18.  f  off  of  15? 

7.  13ix5i?     13.    15|xli?  19.  |of|ofl8f? 

8.  6ix2|?       14.    Ilfx2£?  20.  foffof7|? 

9.  8ix3f?       15.    10fx3£?     21.    f  of  J  of  8^? 
10.    16fx4i?     16.    7jx2£?       22.    $  off  of  60? 

23.  A  man  walked  8^  hours  at  the  rate  of  3f  miles 
per  hour.     How  far  did  he  go? 

24.  How  much  will  4|  dozen  eggs  cost  at  13^  cents 
per  dozen? 

25.  If  a  horse  eats  1^  tons  of  hay  per  month,  how 
much  will  the  hay  for  3^  months  cost,  at  $  20  per  ton  ? 

26.  If  a  box  of  oranges  costs  $  3f ,  how  much  will  5^ 
boxes  cost  ? 

27.  If  a  man  earns  $  2|  per  day,  how  much  does  he 
earn  in  3 J  days? 

28.  A  grocer  sold  18|  barrels  of  apples  at  $  2|  per 
barrel.     How  much  did  he  get  for  them? 


68  FRACTIONS 

29.  A  lady  bought  9^  yards  of  silk  at  |1|  per  yard. 
How  much  did  it  cost  her? 

30.  I  bought  6£  cords  of  wood  at  $4|  per  cord,  and 
paid  for  it  in  rye  at  50  cents  a  bushel.  How  many 
bushels  were  required  to  pay  the  bill? 

31.  How  many  times  8  is  the  product  of  13J  by  4£? 

32.  Jane  is  6|  years  old,  and  her  mother  is  5£  times 
as  old.     How  old  is  her  mother? 

33.  John  earns  $1\  per  day,  and  his  father  earns  3| 
times  as  much.     How  much  does  each  earn  in  8  days? 

34.  If  coal  is  $4-|  a  ton,  and  a  cord  of  wood  costs 
1£  times  as  much,  what  is  the  cost  of  10  tons  of  coal 
and  10  cords  of  wood? 

35.  One  bushel  of  wheat  is  worth  2£  bushels  of  corn. 
How  much  corn  are  1\  bushels  of  wheat  worth? 

36.  A  man  who  owned  f  of  a  field  containing  13^ 
acres,  sold  |  of  what  he  owned.  How  much  did  he 
sell? 

37.  A  man  who  gets  S16|  per  week  has  his  salary 
advanced  to  1|  times  that  sum.  How  much  does  he 
then  receive  per  week  ? 

38.  If  a  man  can  hoe  £  of  an  acre  of  potatoes  in  a 
day,  how  many  acres  can  he  hoe  in  8^  days? 

39.  If  an  acre  of  land  produces  40J  bushels  of  corn, 
how  much  will  2|  acres  produce  ? 

40.  What  will  be  the  cost  of  f  of  a  piece  of  cloth 
containing  12^  yards,  at  $3£  per  yard? 


FRACTIONS  69 

31.   1.    How  many  times  is  f  contained  in  2? 

Solution:  —  2  is  equal  to  f ;  f  is  contained  in  f,  3  times. 
Or,  i  is  contained  in  1  three  times,  and  in  2  six  times.     Hence  § 
is  contained  in  2  one  half  of  6  times  or  3  times.     Therefore,  etc. 

2.  How  many  times  is  J  contained  in  1?  in  3? 
in  2?  in  5?  in  8?  in  7?  in  12? 

3.  How  many  times  is  \  contained  in  6?  in  4? 
in  7?  in  8?  in  24?  in  15?  in  11?  in  10? 

4.  How  many  times  is  f  contained  in  4?  in  2? 
in  6?  in  9?  in  3?  in  10?  in  7? 

5.  Divide4byf;  by  f;  by  f ;  by  \  ;  by  \  ;  by  f . 

6.  Divide  5byl|;  by  2  \  ;   by  If;   by  If  ;   by  3|; 

by  2i. 

7.  If  I  burn  §  of  a  ton  of  coal  per  month,  how  long 
will  6  tons  last  ? 

8.  When  $  |  a  pound  is  charged  for  coffee,  how  many 
pounds  can  be  bought  for  $  3  ? 

9.  A  man  can  plow  §  of  an  acre  of  ground  in  a 
day.  How  long  will  it  take  him  to  plow  a  field  of  10 
acres  ? 

10.  At  $|  per  pound,  how  many  pounds  of  tea  can 
be  bought  for  $9? 

11.  If  a  lady  pays  $f  for  one  yard  of  velvet,  how 
many  yards  can  she  buy  for  $  8  ? 

12.  Divide  ^  into  3  equal  parts  ;  that  is,  divide  £  by  3. 

Solution  :  —  Since  f  is  to  be  divided  into  3  equal  parts,  each 
part  will  be  i  of  J,  which  is  TV 

Or,  to  divide  a  number  by  3  is  to  find  J  of  it;  therefore  to 
divide  f  by  3  is  to  find  J  of  f,  which  is  TV     Therefore,  etc. 


70  FRACTIONS 

13.  How  many  times  is  2  contained  in  -|?  in  f  ? 
in  f  ?  in  If?  in  -If?  in  T\?  in  ty? 

14.  How  many  times  is  3  contained  in  £?  in  f  ? 
in^?  in  If?  inf?init?in«?inft? 

15.  Divide£by2;  by4;  by  3 ;  by  5 ;  by  8  ;  by  6. 

16.  Divide  f  by  3  ;  by  2  ;  by  4  ;  by  7  ;  by  9  ;  by  5. 

17.  Divide  If  by  5;   by  8;    by  10 ;    by  4;    by  3. 

18.  A  man  divided  |  of  an  acre  of  land  into  3  lots. 
What  part  of  an  acre  did  each  contain  ? 

19.  If  4  books  cost  $  Jf ,  how  much  did  each  cost  ? 

20.  If  |  of  a  barrel  of  flour  is  divided  equally  among 
3  families,  how  much  will  each  family  receive  ? 

21.  $-|  was  divided  equally  among  5  boys.  What 
part  of  a  dollar  did  each  receive  ? 

22.  A  man  gave  each  of  his  5  sons  an  equal  share  of 
£  of  his  estate.  What  part  of  the  whole  did  each 
receive  ? 

23.  How  many  times  is  f  contained  in  f  ? 

Solution:  — f  =  As  an<l  I  =  A-  A  *s  contained  in  T92,  f  or  1£ 
times. 

Or,  {  is  contained  in  1  three  times,  and  f  is  contained  in  1  one 
half  of  three  times,  or  f  times.  Since  f  is  contained  in  1,  §  times, 
in  J  it  will  be  contained  f  of  f  times,  or  f  or  1\  times.  Therefore 
f  is  contained  in  f ,  1\  times. 

24.  How  many  times  is  ^  contained  in  |  ?     £  in  \  ? 

25.  How  many  times  is  f  contained  in  £?  in  |? 
in£?in$?in^?inf?  in  ft? 

26.  How  many  times  is  f  contained  in  £?  in  f  ? 
in  f ?  in  ^?  in  $|?  in  |?  in  f  ?  in  fj? 


FRACTIONS 


71 


27.  How  many  times  is  \  contained  in  2|  ?   in  4J  ? 
in  7J?  in  3J?  in  61?  in  8J?  in  5f? 

28.  Divide£by£;  by  f  ;  by  T\  ;  byf;  by  £ 

29.  Divide  2J  by  §  ;  by  1J  ;  by  91 ;  by  2| ;  by  21. 

30.  At  $|  a  pound,  how  many  pounds  of  tea  can  be 
bought  for  $f? 

31.  At  $|  a  box,  how  many  boxes  of  figs  can  be 
bought  for  |3$  ? 

32.  How  many  times  will  5|  gallons  of  kerosene  fill 
a  can  that  holds  J  of  a  gallon  ? 

33.  At  $T3g  a  yard,  how  many  yards  of  cambric  can 
be  bought  for  8  J? 

34.  If  a  man  chops  1^  cords  of  wood  in  a  day,  how 
many  days  will  it  take  him  to  chop  2|  cords? 

Find  the  value  of : 


35. 

f+6. 

45. 

ft  +  8. 

55. 

7-|, 

36. 

tt+A 

46. 

Hi  -e- 

56. 

1&-I- 

37. 

9$ +  5. 

47. 

4|+7. 

57. 

24  +  8J. 

38. 

63  +  f 

48. 

f  -§• 

58. 

10  *f 

39. 

TO  ■*"  $■ 

49. 

2*-*. 

59. 

1-4. 

40. 

*-*• 

50. 

2|-T. 

60. 

if -6. 

41. 

2§  +  3i. 

51. 

9  +  f. 

61. 

ioff-Kf 

42. 

ft-*-* 

52. 

5^11. 

62. 

J-|off 

43. 

18  +  |. 

53. 

20    •    5- 

63. 

foflf  +  f. 

44. 

*-f- 

54. 

16§  h-  10. 

64. 

2f  +  Joflj 

65.    If  one  fish  weighs  1|  pounds,  how  many  such 
fishes  will  weigh  10^  pounds  ? 


72  FRACTIONS 

66.  At  $-$■  per  bushel  for  barley,  how  many  bushels 
can  be  bought  for  $20? 

67.  How  much  does  one  pound  of  sugar  cost,  if  6 
pounds  cost  $1£? 

68.  If  3  apples  cost  4  cents,  how  many  apples  can  be 
bought  for  16  cents  ? 

69.  How  many  dozen  writing  books  at  $£  per  dozen 
can  be  bought  for  $  7 J  ? 

70.  At  $-^%  per  pound,  how  much  rice  can  be  bought 
for$2£? 

71.  If  $  13 J  is  paid  for  2^  dozen  handkerchiefs,  how 
much  does  one  handkerchief  cost? 

72.  How  many  bushels  of  apples  can  be  bought  for 
$  22  at  If  dollars  a  bushel  ? 

73.  A  man  walked  16  miles  in  3£  hours.  What  was 
his  rate  per  hour  ? 

74.  If  a  man  gets  $  3^  per  day,  and  saves  f  of  it,  how 
long  will  it  take  him  to  save  $  30  ? 

75.  If  a  piece  of  work  can  be  done  by  one  man  in 
9£  days,  how  long  will  it  take  4  men  to  do  it  ? 

76.  If  3|  times  a  certain  number  is  6|,  what  is  the 
number  ? 

77.  How  far  can  a  man  travel  in  4|  hours,  if  he  goes 
lOf  miles  in  2|  hours  ? 

78.  A  lady  paid  $  16^  for  a  dress,  and  this  sum  was  4* 
.times  as  much  as  she  had  left.  How  much  had  she  at 
first? 

79.  After  reading  %  of  a  book  there  are  160  pages 
unread.     How  many  pages  are  there  in  the  book  ? 


FRACTIONS  78 

80.  What  is  the  circumference  of  a  wheel  that  turns 
3f  times  in  going  45  feet  ? 

81.  A  horse  was  sold  for  $175,  which  was  If  times 
what  he  cost.     How  much  did  he  cost  ? 

82.  A  grocer  sells  If  pounds  of  butter  for  what  2 
pounds  cost  him.  How  much  does  he  pay  for  it  per 
pound,  if  he  sells  it  at  24  cents  a  pound  ? 

83.  If  a  dairyman  can  make  3^  pounds  of  cheese 
from  15|  quarts  of  milk,  how  much  milk  will  yield  a 
pound  of  cheese  ? 

84.  How  much  will  4  oranges  cost  if  10  oranges  cost 
25  cents? 

85.  When  you  can  get  15  eggs  for  25  cents,  how 
much  will  a  dozen  cost  ? 

86.  If  eggs  at  $ ^  a  dozen  are  exchanged  for  potatoes 
at  1 1  a  bushel,  how  many  eggs  will  pay  for  16  bushels 
of  potatoes  ? 

87.  If  3  men  can  do  a  piece  of  work  in  4^  days,  how 
long  will  it  take  1  man  to  do  it  ?  How  long  will  it  take 
7  men? 

88.  If  3J  pounds  of  rice  cost  25  cents,  how  much  will 
1  pound  cost  ?     How  much  will  14  pounds  cost  ? 

89.  A  gallon  of  cider  cost  $  J.  How  much  cider  can 
be  bought  for  $  If? 

90.  How  far  can  a  man  walk  in  10  hours  whose 
rate  of  walking  is  10  miles  in  3^  hours? 

91.  If  a  horse  eats  f  of  a  bushel  of  oats  in  a  day,  in 
how  many  days  will  he  eat  9  bushels  ? 


74  FRACTIONS 

32.   1.    After  a  boy  lost  |  of  his  marbles,  he  had  36 
left.     How  many  had  he  at  first  ? 

2.  A  man  owned  |  of  a  mill,  and  sold  |  of  his  share 
for  $  6000.     What  was  the  value  of  the  mill  ? 

3.  When  I  have  paid  my  grocer  |  of  his  bill,  I  still 
owe  him  $48.     What  is  his  entire  bill  ? 

4.  If  milk  is  worth  ^  as  much  as  cream,  how  much 
is  cream  worth  when  milk  is  6  cents  a  quart  ? 

5.  A  boy  sold  f  of  the  chestnuts  he  had  gathered. 
The  amount  he  received  was  $  3|.  How  much  were  they 
all  worth  at  the  same  rate  ? 

6.  If  |  of  a  bushel  of  apples  is  worth  £  of  a  bushel 
of  peaches,  how  much  are  peaches  worth  when  apples 
are  90  cents  a  bushel  ? 

7.  If  ^  of  |  of  a  number  is  60,  what  is  the  number  ? 

8.  The  difference  between  |  of  a  number  and  |  of 
it  is  120.     What  is  the  number  ? 

9.  For  4|  pounds  of  meat  I  pay  22  cents  more  than 
for  3|  pounds.     How  much  is  it  per  pound  ? 

10.  A  barrel  of  oil  was  sold  for  $  9,  which  was  1| 
times  its  cost.     How  much  did  it  cost  ? 

11.  A  plot  of  ground  contains  18|  square  rods.     If 
$225  was  paid  for  f  of  it,  how  much  was  that  a  sq.  rd.? 

12.  A  conductor  gets  64  cents  for  a  trip  of  2|  hours. 
At  what  rate  is  he  paid  per  hour  ? 

13.  If  a  horse  was  sold  for  -|  of  his  cost,  what  was 
the  cost  of  the  horse  if  the  selling  price  was  $  196  ? 

14.  If  |  of  a  cord  of  wood   costs  $2|,  how  much 
must  be  paid  for  5  cords  ? 


FRACTIONS  75 

15.  If  3  yards  of  cloth  cost  $4£,  how  many  yards  can 
be  bought  for  $14? 

16.  A  farmer  fed  4J  bushels  of  oats  to  2  horses  in  3 
days.     How  much  did  each  horse  eat  daily  ? 

17.  How  many  suits  of  3|  yards  each  can  be  cut 
from  a  piece  of  cloth  containing  45  yards  ? 

18.  A  is  45  miles  ahead  of  B,  and  travels  9  miles  per 
hour.  If  B  travels  1|  times  as  fast  as  A,  in  how  many 
hours  will  B  overtake  A  ? 

19.  If  4  men  can  do  a  piece  of  work  in  8|  days,  in 
how  many  days  can  1  man  do  the  same  work  ?  In  how 
many  days  can  13  men  do  it  ? 

20.  After  paying  out  §  of  my  money  and  §  of  the  re- 
mainder I  had  $20  left.     How  much  had  I  at  first  ? 

21.  A  man  paid  §  as  much  for  his  chain  as  for  his 
watch.  If  they  both  together  cost  him  $  150,  how  much 
did  he  pay  for  each  ? 

22.  If  $10  is  paid  for  3  yards  of  velvet,  how  much 
can  be  bought  for  $8  ? 

23.  When  3  tons  of  coal  cost  as  much  as  5  cords 
of  wood,  how  much  per  ton  is  coal  if  wood  is  $4|  a 
cord? 

24.  If  J  of  A's  age  is  added  to  J  of  his  age,  the  sum 
is  35  years.     How  old  is  he  ? 

25.  After  a  man  has  traveled  5  hours  at  the  rate  of 
4 J  miles  per  hour,  he  has  still  |  of  the  distance  to  go 
to  complete  the  journey.     How  far  did  he  intend  to  go  ? 

26.  If  I  pay  as  much  for  3  turkeys  as  for  7  chickens, 
how  much  are  turkeys  worth  when  3  chickens  cost  914? 


76  FRACTIONS 

27.  If  rice  is  sold  for  7  cents  a  pound  when  it  costs 
$8f  a  barrel,  for  how  much  should  it  be  sold  when  it 
costs  $11 J  a  barrel? 

28.  If  3£  acres  produce  8$  tons  of  hay,  how  many 
tons  will  8  acres  produce  ? 

29.  A  horse  travels  50  miles  in  6§  hours.  How  long 
will  it  take  him  to  travel  40  miles  ? 

30.  If  a  horse  eats  §  of  a  ton  of  hay  in  §  of  a  month, 
how  long  will  2^  tons  last  him  ? 

31.  A  man  expended  §  of  his  money  for  a  horse  and 
$  as  much  for  a  carriage.  He  then  had  $  110  left.  How 
much  had  he  at  first  ? 

32.  A  lady  bought  some  muslin,  and  later  bought 
1|  times  as  much.  She  then  used  §  of  all  she  had, 
and  had  32  yards  left.     How  much  did  she  buy  at  first  ? 

33.  Gloves  that  cost  $1§  a  pair  were  sold  for  1J 
times  their  cost.  How  many  pairs  must  be  sold  to 
gain  $22? 

34.  John  earns  $|  a  day,  and  his  father  1£  times  as 
much.     In  how  many  days  can  they  together  earn  $27  ? 

35.  If  4  horses  eat  2|  bushels  of  oats  per  day,  how 
long  will  that  quantity  last  3  horses  ? 

36.  If  a  man  can  row  a  boat  down  stream  at  the 
rate  of  8  miles  an  hour,  and  his  rate  of  rowing  up  stream 
is  |  of  his  rate  down,  how  far  can  he  row  and  return  in 
39  hours? 

37.  If  3 J  bushels  of  apples  cost  $5|,  how  much  will 
5  bushels  cost? 


FRACTIONS  77 

38.  From  1 J  pounds  of  ham  20  sandwiches  are  made, 
and  sold  at  5  cents  each.  How  much  is  received  per 
pound  for  the  ham  if  the  bread  and  butter  used  are 
worth  25  cents? 

39.  A  farmer  paid  |  of  $  10  for  clover  seed  at  $  2\  a 
bushel.     How  many  bushels  did  he  buy? 

40.  A  grocer  gave  1|  gallons  of  molasses  for  6 
pounds  of  butter  at  17  \  cents  a  pound.  How  much 
was  the  molasses  worth  per  gallon? 

41.  A  expends  $  of  his  money,  and  then  earns  J  as 
much  as  he  has  left.  He  then  has  145.  How  much 
had  he  at  first  ? 

42.  A  and  B  ride  from  the  same  point  in  opposite 
directions,  A  at  the  rate  of  13|  miles  in  1J  hours,  and 
B  at  the  rate  of  13^  miles  in  2|  hours.  How  far  apart 
will  they  be  in  5  hours? 

33.  1.    20  is  |  of  what  number?  30?  24?  18?  50? 

2.  24  is  |  of  what  number?  36?  30?  27?  90?  60? 

3.  40  is  |  of  what  number?  48?  32?  16?  24?  120? 

4.  28  is  }  of   what  number?  36?  72?  24?   144? 

5.  21  is  I  of  what  number?  35?  49?  28?  42?  140? 

6.  100  is  f  of  what  number?    80?    75?   45?    65? 

7.  50  is  J^  of  what  number?  70  ?  30  ?  90  ?  60  ? 

8.  36  is  f  of  what  number  ?  48  ?  72  ?  60  ?  42  ? 

9.  48  is  |  of  what  number  ?  64?  96  ?  72  ?  32  ? 

10.  18  is  |  of  what  number  ? 

Solution  : —  Since  18  is  f  of  a  number,  £  of  the  number  is  -^,  and 
the  number  is  5  times  -^,  or  -9^,  which  is  equal  to  22| .    Therefore,  etc. 

11.  12  is  |  of  what  number?  9?  6?  13?  16?  19? 


78  FRACTIONS 

12.  7  is  §  of  what  number?  9?  11?  13?  19?  23? 

13.  22isf  of  what  number?  17?  11?  13?  40?  100? 

14.  24  is  f  of  what  number?  32?  17?  13?  22?  14? 

15.  7  is  f  of  what  number?  8?  13?  16?  20?  40? 

16.  5  is  \  of  what  number?  11?  4?  9?  13?  17? 

17.  15  is  f  of  how  many  times  5? 

Solution  :  —  Since  15  is  f  of  25,  it  is  {  of  5  times  5.  There- 
fore, etc. 

18.  24  is  £  of  how  many  times  6?  36?  60  ?  48?  12? 

19.  24  is  §  of  how  many  times  5?  20?  36?  40?  50? 

20.  9  is  f  of  how  many  times  4?  12?  24?  36?  18? 

21.  $42  is  |  of  what  I  paid  for  wood  at  $7  per  cord. 
How  many  cords  were  there  ? 

22.  $150  is  |  the  cost  of  some  cattle  at  $75  per  head. 
How  many  cattle  were  there? 

23.  $9|  is  |  of  what  was  paid  for  8  tons  of  coal. 
How  much  did  it  cost  per  ton  ? 

24.  A  man  paid  $18|  for  a  cow,  which  was  -fa  of 
what  he  paid  for  a  horse.  How  much  did  the  horse 
cost? 

25.  A  man  plowed  5^  acres  of  ground  at  SI}  per 
acre,  and  what  he  received  was  \^  of  what  he  already 
had.     How  much  money  did  he  then  have  ? 

26.  A  man  after  traveling  3  days,  averaging  30^ 
miles  per  day,  had  accomplished  only  ^  of  his  entire 
journey.     How  far  had  he  yet  to  go  ? 

27.  A  merchant  was  obliged  to  sell  a  piece  of  cloth 
for  $  16^,  which  was  £  of  what  it  cost  him.  How  much 
did  he  lose  ? 


FRACTIONS  79 

28.  A  merchant  sold  6  yards  of  silk  at  $  3|  per  yard. 
What  he  received  for  it  was  ^_.  0f  the  value  of  what  he 
had  left  at  $  3f  per  yard.     How  much  had  he  left  ? 

29.  $18-|  is  f  of  what  was  paid  for  3  tons  of  hay. 
How  much  was  the  hay  per  ton  ? 

30.  10  J  yards  of  ribbon  is  £  of  8  times  what  Mary 
used  to  trim  her  dress.  How  much  did  it  cost  at  45 
cents  a  yard? 

31.  5^  miles  is  f  of  6  times  the  distance  John  can 
travel  in  an  hour.     How  far  can  he  travel  in  an  hour  ? 

34.  1.    |  of  12  is  how  many  sevenths  of  21? 

Solution  :  —  f  of  12  =  9 ;  and  9  is  as  many  sevenths  of  21  as 
\  of  21  is  contained  times  in  9,  which  is  3.  Therefore  §  of  12  is 
f  of  21. 

2.  |-  of  56  is  how  many  fifths  of  25? 

3.  |  of  24  is  how  many  tenths  of  40  ? 

4.  £  of  72  is  how  many  sevenths  of  28  ? 

5.  ^  of  140  is  how  many  fifths  of  35  ? 

6.  \^  of  75  is  how  many  thirds  of  33  ? 

7.  f  of  11 J  is  how  many  sevenths  of  21  ? 

8.  %  of  11 J  is  how  many  sixths  of  18  ? 

9.  |  of  171  is  how  many  fifths  of  25  ? 

10.  &  of  12f  is  how  many  halves  of  14  ? 

11.  |  of  18|  is  how  many  thirds  of  21  ? 

12.  £  of  30  is  how  many  eighths  of  64  ? 

13.  -|  of  14f  is  how  many  fifths  of  15  ? 

14.  £  of  9£  is  how  many  halves  of  22  ? 
16.  |  of  9|  is  how  many  thirds  of  51  ? 


80  FRACTIONS 

16.  6  times  33£  is  how  many  halves  of  80  ? 

17.  f  of  20£  is  |  of  what  number  ? 

Solution  :  —  j  of  20J  =  9,  and  9  is  f  of  15.    Therefore,  etc* 

18.  |  of  18f  is  f  of  what  number  ? 

19.  f  of  33£  is  §  of  what  number  ? 

20.  f  of  22|  is  |  of  what  number  ? 

21.  ^of  15|  is  f  of  what  number? 

22.  f  of  7£  is  J{J  of  what  number? 

23.  f  of  16 J  is  if  of  what  number? 

24.  |  of  13|  is  f  of  what  number  ? 

25.  |  of  13f  is  f  of  what  number? 

26.  £  of  4£  yards  of  ribbon  was  f  of  the  number  of 
yards  of  ribbon  that  Amy  bought  at  40  cents  a  yard. 
How  much  did  it  cost  ? 

27.  If  |  of  f  16|  was  §  of  what  a  man  paid  for  4  tons 
of  hay,  how  much  was  it  per  ton  ? 

28.  If  %  of  5|  miles  is  -^  of  the  distance  that  John 
walked  in  2  hours,  what  was  his  rate  per  hour  ? 

29.  If  1|  times  7^  miles  is  §  of  the  distance  from  A 
to  B,  how  far  is  it  ? 

30.  If  I  paid  |  of  $  22±  for  3f  tons  of  coal,  how  much 

was  it  per  ton  ? 

35.  1.  If  I  had  twice  as  much  money  as  I  have,  -fe 
of  it  would  be  $  25.     How  much  money  have  I  ? 

2.  If  |  of  2^  times  the  distance  from  New  York 
to  Philadelphia  is  135  miles,  what  is  the  distance  ? 

3.  A  farmer  sold  f  of  his  hay  at  $  15  a  ton  and  re- 
ceived for  it  $  6.     How  much  hay  had  he  ? 


FRACTIONS  81 

4.  |  of  a  piece  of  ribbon  was  sold  at  12  cents  a 
yard,  for  45  cents.  How  many  yards  of  ribbon  were 
there  in  the  piece  ? 

5.  The  list  price  of  a  piano  was  $  300.  T2^  of  this 
price  is  §  of  the  deduction  that  was  made  when  it  was 
sold.     How  much  was  received  for  it  ? 

6.  A  man  paid  $1200  for  a  lot;  §  of  3£  times  the 
cost  of  the  lot  was  f  of  the  cost  of  the  house  he  built 
upon  it.     How  much  did  the  house  cost  ? 

7.  The  distance  from  New  York  to  Chicago  is  ap- 
proximately 1000  miles.  -|  of  this  distance  is  4  times 
the  distance  from  Boston  to  Albany.  How  far  is  it 
from  Boston  to  Albany  ? 

8.  In  a  certain  field  there  are  99  head  of  cattle;  f 
of  the  number  of  cattle  is  equal  to  §  of  the  number  of 
acres  of  land  in  the  field.  What  is  the  value  of  the 
field  at  1100  per  acre? 

9.  A  man  pays  $300  a  year  rent,  and  |-  of  this  sum 
is  |  of  T^  of  his  salary  per  year.     What  is  his  salary  ? 

10.  A  man  being  asked  his  age  said  that  |  of  his  age 
was  f  of  40  years.     How  old  was  he  ? 

11.  How  much  must  be  paid  for  3|  tons  of  hay  if  | 
of  3f  tons  cost  $  37J  ? 

12.  A  boy  expended  f  of  his  money  and  then  earned 
f  as  much  as  he  expended.  He  then  had  $  14.  How 
much  had  he  at  first  ? 

13.  The  goods  in  a  store  are  worth  $2000.  -£  of 
their  value  is  §  of  twice  the  value  of  the  store.  What 
is  the  value  of  the  store  ? 

MILNE    MENTAL 6 


82  FRACTION'S 

14.  A  hardware  dealer  sells  lemon  squeezers  at  $  27 
per  dozen.  f  of  this  sum  is  £  of  what  they  cost  per 
dozen.     What  is  his  gain  per  dozen  ? 

15.  My  age  increased  by  f  of  2£  times  my  age  is  80 
years.     How  old  am  I  ? 

16.  After  a  man  has  traveled  |-  of  |  of  the  distance 
he  has  to  go,  he  has  still  25  miles  to  travel.  What  is 
the  length  of  his  journey  ? 

17.  A  horse  costs  $  150,  and  ^  of  f  of  this  is  the  value 
of  two  cows.     What  are  th^  cows  worth  apiece  ? 

18.  If  a  lemon  costs  £  as  much  as  an  orange,  and  a 
dozen  of  each  cost  together  54  cents,  how  much  is  each 
worth  apiece  ? 

19.  Iff  of  3|  pounds  of  rice  cost  f  of  §  of  40  cents, 
how  much  is  rice  per  pound  ? 

20.  If  2§  tons  of  coal  cost  £  of  $13£,  how  much  is 
that  per  ton  ? 

36.     1.    What  part  of  5  is  3  ? 

Solution  :  —  1  is  I  of  5,  and  3  is  3  times  J  of  5,  or  $  of  5. 
Therefore  3  is  §  of  5. 

2.  What  part  of  5  is  4  ?     of  5  is  2  ?     of  7  is  3  ? 

3.  What  part  of  9  is  4  ?     of  10  is  7  ?     of  8  is  5  ? 
of  8  is  7?     of  11  is  3?     of  13  is  6? 

4.  What  part  of  12  is  8?     of  12  is  9  ?     of  10  is 
6?     of  15  is  10?     of  16  is  12? 

5.  What  part  of  18  is  6  ?     of  18  is  10  ?     of  18  is 
14  ?     of  20  is  15  ?     of  25  is  15  ? 

6.  What  part  of  24  is  16?     of  24  is  18  ?     of  28  is 
21?    of  35  is  25?    of  30  is  24? 


FRACTIONS  83 

7.  What  part  of  60  is  40  ?     of  72  is  48  ?     of   90 
is  60  ?     of  100  is  80  ?     of  120  is  90  ? 

8.  What  part  of  f  is  J  ?     of  f  is  f  ?     of  f  is  f  ? 

9.  What  part  of  |  is  f  ?     of  T8T  is  T\  ?     of  if  is 
J>^  ?     of  11  is  -4-  ?     of  -14  is  -4-  ?     of  -9^  is  -4r  ? 

Tl  •       Ui    13  ib  13  •       U1    IT  lb  IT  •       Ui    12   i&  12  ' 

10.  What  part  of  2\  is  f  ?     of  3 J  is  11?     of  2|  is 
|?     of  3f  is2£?     of  2f  isli? 

11.  What  part  of  f  is  f  ? 

Solution  :  —  §  =  T92,  and  f  =  T% ;  T%  =  f  of  TV 
Therefore  §  is  f  of  f . 

12.  What  part  of  f  is  l?     of  §  is  1?     of  f  is  f  ? 

13.  What  part  of  f  is  f  ?     of  $  is  l?     of  |  is  f  ? 
oflisl?     of  |  is  J?     offisi? 

14.  What  part  of  2|  is  11?     of  31  is  If?     of   3f 
is  21?     of  5iis3|?     of  3|is2i? 

37.     1.    If   8    sheep    cost  $20,   how   much   will    6 
sheep  cost? 

Solution:  —  Since  6  sheep  are  f  of  8  sheep,  they  will  cost  f  of 
$20,  or  $15.     Therefore,  etc. 

2.  How  much  will  15  loads  of  sand  cost  if  10  loads 
cost  $21? 

3.  If  9  oranges  cost   30   cents,  how  much  will   6 
oranges  cost  ? 

4.  A  train  runs  at  the  rate  of  50  miles  an  hour. 
How  far  will  it  run  in  48  minutes  ? 

5.  A  ball  cost  75  cents,  and  a  bat  cost  45  cents. 
What  part  of  the  cost  of  the  ball  was  that  of  the  bat  ? 


84  FRACTIONS 

6.  John  receives  If  dollars  a  day,  and  his  father 
$2 J.  They  work  each  the  same  number  of  days,  and 
John's  pay  amounts  to  $42.  How  much  should  his 
father  receive  ? 

7.  If  3f  acres  of  land  cost  $  600,  how  much  should 
6J  acres  cost  at  that  rate  ? 

8.  The  hay  on  1|  acres  of  land  amounted  to  3§  tons. 
At  that  rate,  how  much  would  5^  acres  yield  ? 

9.  If  3  men  can  earn  $11 J  in  a  certain  time,  how 
much  can  7  men  earn  in  the  same  time  ? 

10.  A  farmer  sold  §  of  |  of  a  flock  of  sheep  for  $80. 
What  was  the  remainder  of  the  flock  worth  if  it  was 
sold  at  the  same  rate  ? 

11.  If  3 1  tons  of  straw  cost  $11|,  how  much  will  2| 
tons  cost  at  the  same  rate  ? 

12.  If  a  man  can  row  13 J  miles  in  2|  hours,  how  far, 
at  that  rate,  can  he  row  in  4  J  hours  ? 

13.  If  $  9f  will  pay  for  1|  cords  of  wood,  how  much 
wood  can  be  bought  for  $  39  ? 

14.  A  barrel  of  flour  can  be  bought  for  $5§.  What 
part  of  a  barrel  can  be  bought  for  $8£  ? 

15.  If  4  men  can  do  a  piece  of  work  in  6  days,  how 
long  will  it  take  3  men  to  do  it  ? 

16.  If  a  man  can  do  a  piece  of  work  in  16  days, 
working  10  hours  a  day,  how  long  will  it  take  him  to 
do  it  if  he  works  8  hours  a  day  ? 

17.  If  4  horses  can  eat  3|  tons  of  hay  in  one  month, 
how  long  will  8  tons  last  10  horses  ? 


FRACTIONS  85 

18.  If  a  barrel  of  flour  will  last  a  family  of  6  per- 
sons 4^  weeks,  how  long  will  it  last  a  family  of  4 
persons  ? 

19.  If  a  horse  can  eat  If  bushels  of  oats  in  a  week, 
how  long  will  24  bushels  last  8  horses  ? 

20.  A  merchant  exchanged  6J  yards  of  silk  at  $1| 
per  yard  for  12§  bushels  of  wheat.  At  that  rate  what 
was  the  cost  of  the  wheat  per  bushel  ? 

21.  John  earns  $-|  as  often  as  James  earns  $f .  When 
together  they  have  earned  $93,  how  much  has  each 
earned  ? 

22.  Two  persons  start  at  the  same  time  and  travel 
toward  each  other,  one  at  3  miles  per  hour,  and  the 
other  at  4|  miles  per  hour.  When  they  meet,  one  has 
traveled  30  miles  farther  than  the  other.  How  far 
apart  were  they? 

23.  A  can  do  a  piece  of  work  in  2  days.  What  part 
of  it  can  he  do  in  1  day  ?  If  B  can  do  the  same  piece 
of  work  in  3  days,  what  part  of  it  can  he  do  in  1  day  ? 
What  part  can  both  together  do  in  1  day?  If  both 
together  could  do  ^  of  it  in  1  day,  how  many  days 
.would  it  take  them  to  do  it  all  ?  Since  both  together 
can  do  f  of  it  in  one  day,  how  many  days  will  it  take 
them  to  do  it  all  ? 

24.  A  can  do  a  piece  of  work  in  5  days,  and  B  can 
do  it  in  6  days.     How  long  will  it  take  both  to  do  it  ? 

25.  A  and  B  can  do  a  piece  of  work  in  4  days.  If 
A  can  do  it  in  6  days,  how  long  will  it  take  B  ? 

26.  If  a  boy  can  ride  a  bicycle  16  miles  in  1|-  hours, 
how  far,  at  that  rate,  can  he  ride  in  4|  hours  ? 


86  FRACTIONS 

27.  In  a  certain  school  |  of  |  of  the  pupils  are  boys. 
How  many  girls  are  there  if  the  school  contains  60 
pupils  ? 

28.  A  man  can  do  a  piece  of  work  in  9  days.  How 
much  should  he  receive  for  3^  days'  work,  if  he  gets 
1 35  for  the  whole? 

29.  If  -J-  of  a  thousand  feet  of  lumber  cost  $  8-| ,  how 
much  should  be  paid  for  |  of  a  thousand  feet? 

30.  A  farmer  sold  f  of  a  farm  at  $40  an  acre  for 
$500.     How  many  acres  were  there  in  the  farm  ? 

31.  A  can  earn  $10  in  2\  days,  and  B  in  3J  days.  In 
how  many  days  can  they  together  earn  $  48  ? 

32.  A  can  do  a  piece  of  work  in  4  days,  and  B  can 
do  it  in  7  days.  How  long  will  it  take  both  together 
to  do  the  work  ? 

33.  A  can  do  a  piece  of  work  in  2  days,  B  can  do  it 
in  3  days,  and  C  can  do  it  in  4  days.  In  how  many 
days  can  all  together  do  the  work  ? 

34.  A  can  do  a  piece  of  work  in  2J  days,  and  B  can 
do  it  in  3 J  days.  If  they  work  together  until  it  is  com- 
pleted and  earn  $  24,  how  much  should  each  receive  ? 

Solution  :  —  Since  A  can  do  the  work  in  2£  days,  he  can  do  §  of. 
the  work  per  day,  and  since  B  can  do  the  work  in  3£  days,  he  can 
do  ^  of  the  work  per  day.  Both  working  together  can  therefore 
do  f  +  f ,  or  §f ,  of  the  work  per  day.  Since  A  does  f ,  or  if,  of  the 
work  per  day,  and  both  together  do  f f  of  the  work  per  day,  A 
does  J|  of  the  work  done  by  both  each  day,  and  consequently  he 
is  entitled  to  Jf  of  $24,  the  sum  earned,  which  is  $14.  B's  share 
is  therefore  Jj  of  $24,  or  $  10. 

35.  A  can  do  a  piece  of  work  in  1J  days,  and  B  can 
do  it  in  2 \  days.  If  they  work  together  until  it  is  com- 
pleted and  earn  $  6,  how  much  should  each  receive  ? 


FRACTIONS  87 

36.  A  can  do  a  piece  of  work  in  2|-  days,  and  B  can 
do  it  in  3^  days.  If  they  work  together  until  it  is  com- 
pleted, and  earn  $6.70,  how  much  should  each  receive  ? 

37.  If  5  men  can  do  a  piece  of  work  in  3|  days,  in 
what  time  can  3  men  do  the  same  work  ? 

38.  For  every  $2  A  has,  B  has  $3.  Together  they 
have  $120.     How  much  has  each? 

39.  If  you  increase  a  certain  number  by  26  more 
than  ^  of  it,  the  sum  will  be  104.  What  is  the  num- 
ber ? 

40.  Charles  had  3J  times  as  much  money  as  James. 
He  spent  half  his  money  and  earned  $  5  and  then  both 
together  had  $  60.     How  much  had  each  ? 

41.  After  selling  ^  of  my  chickens  and  J  of  the  re- 
mainder I  had  30  left.     How  many  had  I  at  first  ? 

42.  If  3  men  do  a  piece  of  work  in  10  days,  how 
long  will  it  take  2  men  to  do  a  piece  of  work  twice  as 
great  ? 

43.  A  earns  $  5  per  day,  and  B  earns  $4  per  day.  At 
the  end  of  a  certain  time  they  have  together  earned 
$  180.     How  much  has  each  earned  ? 

44.  Three  men  agreed  to  do  £  of  a  piece  of  work,  for 
the  whole  of  which  $  150  was  to  be  paid.  They  worked 
2,  3,  and  7  days  respectively.  How  much  should  each 
receive  ? 

45.  If  apples  are  bought  at  6  for  5  cents,  and  sold  at 
4  for  5  cents,  how  many  must  be  sold  to  gain  50  cents  ? 

46.  A  coal  dealer  sold  ^  of  his  coal,  and  had  100 
•  tons  more  left  than  he  sold.     How  many  tons  had  he 

at  first  ? 


88  FRACTIONS 

47.  A  bicyclist  goes  56  miles  in  4§  hours.  At  that 
rate  how  far  will  he  go  in  5f  hours  ? 

48.  A  is  |  as  old  as  B,  and  B  |  as  old  as  C.  How 
old  is  each,  if  the  sum  of  their  ages  is  108  years  ? 

49.  A  can  plow  3  acres  in  2  days,  and  B  4  acres  in  3 
days.     How  much  can  both  plow  in  12  days  ? 

50.  If  5  pounds  of  lard  are  worth  2  pounds  of  butter, 
how  much  should  be  paid  for  1£  pounds  of  butter,  when 
lard  is  12  cents  a  pound  ? 

51.  Divide  $740  among  A,  B,  and  C,  so  that  A  shall 
have  |  as  much  as  B,  and  B  |  as  much  as  C. 

52.  A  farmer  sold  §  of  his  chickens,  and  then  \  of 
the  remainder,  and  had  90  chickens  left.  How  many 
had  he  at  first? 

53.  A  horse  travels  20  miles  in  1 J  hours.  How  far, 
at  that  rate,  will  he  go  in  4|  hours  ? 

54.  A  father  is  28  years  older  than  his  son.  How 
old  is  each  if  the  son  is  f  as  old  as  his  father  ? 

55.  After  expending  $100,  and  then  earning  |  as 
much  as  he  had  left,  Mr.  Jones  had  $210.  How  much 
had  he  at  first  ? 

56.  Five  sixths  of  my  wages  for  a  month  is  $60  less 
than  J  of  my  wages  for  two  months.  How  much  do  I 
earn  per  month  ? 

57.  If  the  sum  of  §  and  f  of  a  number  is  multiplied 
by  2^,  the  product  is  95.     What  is  the  number  ? 

58.  A  man  bought  ^  of  a  vessel  and  sold  J  of  his 
share  for  $16,000.     At  that  rate,  what  was  the  value  of- 
the  vessel  ? 


FRACTIONS  89 

59.  A  sum  of  money  was  divided  among  three  boys. 
The  first  received  J  of  it,  the  second  -^  of  it,  and  the 
third  $ 60  more  than  the  second.  What  was  the  share 
of  each  ? 

60.  A  grocer  pays  30  cents  per  dozen  for  eggs.  He 
sells  them  so  as  to  gain  5  cents  on  each  25  cents'  worth 
sold.     How  many  does  he  give  for  25  cents  ? 

61.  How  much  corn  at  $f  a  bushel  can  be  bought 
for  $21? 

62.  If  |  of  a  yard  of  broadcloth  costs  $4^-,  how  much 
can  be  bought  for  $  14  ? 

63.  I  bought  a  horse  for  $140,  which  was  |  less  than 
its  value,  and  sold  it  for  J  more  than  its  value.  How 
much  was  the  gain  ? 

64.  A,  B,  and  C  owned  a  flock  of  sheep,  of  which 
A  owned  J,  B  ^,  and  C  12  more  than  both  A  and  B. 
How  many  sheep  were  there  ? 

65.  How  much  change  is  received  out  of  a  fifty- 
dollar  bill,  after  paying  for  18  bushels  of  cranberries 
at  $ 2  J  per  bushel  ? 

66.  A  sleigh  cost  $  75,  which  was  f  of  5  times  the 
cost  of  the  harness.     How  much  did  the  harness  cost  ? 

67.  A  merchant  sold  8  barrels  of  flour  for  $54, 
and  gained  $1|  per  barrel.  How  much  did  it  cost  him 
per  barrel ? 

68.  A  girl  bought  at  one  time  2|  yards  of  ribbon, 
and  at  another  3J  yards  at  the  same  price  per  yard.  It 
all  cost  $1.     How  much  did  it  cost  per  yard? 

69.  If  31-  yards  of  silk  cost  $20,  how  much  will  16| 
yards  cost? 


90  FRACTIONS 

70.  A  farmer  sold  4  tons  of  his  hay  for  $62,  and 
half  of  the  remainder  at  $  16|  per  ton.  If  he  received 
$  162  for  what  he  sold,  how  much  had  he  at  first  ? 

71.  A  man  sold  3f  cords  of  wood  at  $l-§  per  cord. 
What  he  received  was  1^  times  what  he  paid  for  one 
ton  of  coal.     What  was  the  cost  of  the  coal  per  ton  ? 

72.  A  farmer  paid  $70  for  2  cows.  How  much  did 
each  cost  if  one  cost  §  as  much  as  the  other  ? 

73.  |  of  a  number  increased  by  £  of  §  of  60  is  35. 
What  is  the  number  ? 

74.  Mary  is  20  years  old,  and  f  of  her  age  is  £  of  | 
of  her  sister's  age.     How  old  is  her  sister? 

75.  If  J  of  a  number  is  divided  by  1£,  the  quotient 
will  be  16.     What  is  the  number? 

76.  A  sold  B  a  watch  and  gained  £  of  its  cost.  If  he 
had  received  $5  more,  he  would  have  gained  \  of  its 
cost.     How  much  did  the  watch  cost  ? 

77.  If  a  man  can  drive  45  miles  in  4J  hours,  at  that 
rate  how  long  will  it  take  him  to  drive  75  miles  ? 

78.  A  cistern  has  2  pipes,  one  of  which  can  empty  it 
in  2  hours,  and  the  other  can  fill  it  in  3  hours.  If  the 
cistern  is  full,  and  both  pipes  are  set  running,  in  how 
many  hours  will  it  be  emptied  ? 

79.  A  man  paid  -|  of  his  money  for  an  overcoat,  and 
then  earned  \  as  much  as  he  had  left,  after  which  he 
had  $15  less  than  he  had  at  first.  How  much  did  the 
overcoat  cost? 

80.  A  dealer  sold  5  barrels  of  apples  for  $17 J,  which 
was  |  as  much  as  he  received  for  all  he  had  left  at  $4 
a  barrel.     How  many  barrels  did  he  have  in  aH  ? 


FRACTIONS  91 

81.  Henry  solved  If  times  as  many  problems  as 
William.  Upon  counting  them  it  was  found  that 
Henry  had  solved  12  more  than  William.  How  many 
did  each  solve  ? 

82.  If  a  stick  31-  feet  long  will  cast  a  shadow  of  4J 
feet,  how  long  will  be  the  shadow  of  a  stick  6  feet  long? 

83.  In  an  orchard  J  of  the  trees  are  apple  trees,  \ 
pear  trees,  and  the  remainder  peach  trees.  How  many 
trees  are  there  in  the  orchard,  if  there  are  70  peach  trees  ? 

84.  If  9  men  can  do  a  piece  of  work  in  6|  days,  how 
long  will  it  take  6  men  to  do  the  same  work  ? 

85.  My  horse  cost  8J  times  as  much  as  my  sleigh, 
and  together  they  cost  $360.  What  was  the  cost  of 
each? 

86.  If  |  of  a  yard  of  cloth  costs  $  J,  how  much  will  5| 
yards  cost? 

87.  A  boy  lost  f  of  his  marbles.  He  gave  J  of  the 
remainder  to  his  brother,  and  had  30  marbles  left.  How 
many  had  he  at  first  ? 

88.  One  pedestrian  is  48  steps  ahead  of  another,  and 
goes  3  steps  while  the  other  goes  5.  How  many  steps 
will  the  one  in  advance  go  before  he  is  overtaken,  if  the 
steps  of  both  are  of  equal  length  ? 

89.  If  3J  gallons  of  kerosene  will  last  a  family  2 
weeks,  how  much  will  it  cost  at  12  cents  a  gallon  to 
provide  oil  for  a  family  for  5  weeks  and  3  days  ? 

90.  If  a  horse  eats  |  of  a  ton  of  hay  in  one  month, 
how  much  will  it  cost  to  supply  5  horses  with  hay  for  3 
months  at  $  16  per  ton  ? 


92  FRACTIONS 

91.  If  |  of  a  bushel  of  clover  seed  is  used  to  sow  one 
acre,  how  much  will  it  cost  to  sow  4  acres,  when  clover 
seed  is  $16  per  bushel? 

92.  When  §  of  \  of  my  money  is  $10  less  than  §  of 
my  money,  how  much  have  I  ? 

93.  If  |  of  a  yard  of  cloth  costs  $2f,  how  much  can 
be  bought  for  $27? 

94.  A  can  walk  as  far  in  3J  hours  as  he  can  drive  in 
1^  hours.  At  what  rate  per  hour  does  he  walk,  if  he 
drives  10  miles  per  hour  ? 

95.  Two  trains  going  in  the  same  direction  are  30 
miles  apart.  The  train  behind  gains  upon  the  other 
1£  miles  per  hour.  In  how  many  hours  will  they  be 
together  ? 

96.  A  man  receives  $  100  for  5fy  weeks'  labor.  How 
much  should  he  receive  for  8|-  weeks'  labor  ? 

97.  If  bread  is  sold  at  6  cents  a  loaf  when  flour  is 
$6|  a  barrel,  what  should  be  charged  for  loaves  of  the 
same  size  when  flour  is  $  8|  per  barrel  ? 

98.  If  $  3  is  paid  for  sawing  some  wood  when  the 
sticks  are  sawed  into  2  pieces,  how  much  should  be  paid 
for  sawing  it  when  the  sticks  are  sawed  into  3  pieces  ? 

99.  How  many  barrels  of  cider,  at  $  2|  per  barrel, 
can  be  bought  for  $115? 

100.  If  Mr.  Chadwick  were  2|  times  as  old  as  he  is, 
|  of  his  age  would  be  60  years.     How  old  is  he  ? 

101.  A  man  owns  -|  of  a  farm.  After  selling  10 
acres,  he  owns  ^  of  the  farm.  How  many  acres  are 
there  in  the  farm? 


FRACTIONS  93 

102.  If  3J  cords  of  wood  cost  as  much  as  2J  tons  of 
coal,  how  much  will  10  tons  of  coal  cost  when  wood  is 
$4  a  cord? 

103.  Some  sheep  that  cost  $6  each  were  sold  for 
$  80,  which  was  only  -|  of  their  cost.  How  many  were 
there  ? 

104.  Turkeys  that  were  bought  at  $4  each  were  sold 
for  $10 J  a  dozen.  How  much  was  gained  on  100 
turkeys? 

105.  If  5|  pounds  of  meat  cost  99  cents,  how  much 
will  6f  pounds  cost  ? 

106.  A  man  bought  4|  tons  of  coal  for  $19  and 
sold  2f  tons  at  cost.     How  much  did  he  get  for  it  ? 

107.  If  §  of  \  of  a  number  is  30  more  than  |  of  ^  of 
the  number,  what  is  the  number? 

108.  After  expending  \  of  my  money,  $ 45  is  -|  of 
what  is  left.     How  much  had  I  at  first  ? 

109.  If  6  men  require  3J  days  to  do  a  piece  of  work, 
how  long  will  it  take  7  men  to  do  the  same  work? 

110.  If  Mary  can  make  a  cloak  in  2J  days,  how 
many  cloaks  can  she  make  in  15  days  ? 

111.  How  much  will  \  of  a  ton  of  hay  cost  if  2|  tons 
cost  $33? 

112.  A  boy  sold  -|  of  his  doves  and  then  bought  | 
as  many  as  he  had  sold.  How  many  doves  had  he  at 
first  if  he  then  had  90  ? 

113.  A  man  bought  12  yards  of  sheeting  at  12 J  cents 
a  yard  and  paid  for  it  with  eggs  at  3  for  5  cents.  How 
many  dozen  eggs  did  it  take  ? 


94  FRACTIONS 

114.  By  selling  a  watch  for  1£  times  its  cost  I  shall 
gain  S3  more  than  if  I  sell  it  for  1£  times  its  cost. 
How  much  did  it  cost  ? 

115.  In  a  storm  at  sea  the  mast  of  a  ship  was  broken 
into  three  pieces.  The  piece  left  standing  was  f  as 
long  as  the  middle  piece  and  §  as  long  as  the  end  piece. 
How  long  is  the  piece  left  standing  if  the  sum  of  the 
lengths  of  the  pieces  broken  off  is  84  feet? 

Suggestion  :  —  f  of  the  middle  piece  equals  §  of  the  end  piece. 

116.  In  making  a  journey,  a  man  went  £  of  the  dis- 
tance the  first  day,  §  of  the  remaining  distance  the 
second  day,  and  40  miles  the  third  day.  What  was  the 
length  of  the  journey  ? 

117.  If  5  bushels  of  wheat  cost  $1J  more  than  5 
bushels  of  corn,  what  is  the  price  of  each  per  bushel  if 
one  bushel  of  each  together  costs  $  1  ? 

118.  If  |  of  the  number  of  boys  in  a  school  is  equal 
to  |  of  the  number  of  girls,  and  the  number  of  both  is 
850,  how  many  of  each  are  there? 

119.  After  expending  10  cents  more  than  §  of  my 
money  I  had  80  cents  left.     How  much  had  I  at  first? 

38.   1.    What   part   of   81  is  25  cents?     50  cents? 


75  cents 

;? 

121   cents? 

371 

cents  ? 

621 

cents  ? 

871 

cents?     6J  cents  (one 
(121  cents  -f  6\  cents) 
cents?     8^  cents? 

half  o 
?     33^ 

f  121  cents)' 
cents?     66| 

?     18| 

cents? 

cents 
16j 

2.    What  will  be  the  cost  of  144  dozen  eggs  at  121 
cents  per  dozen? 

Suggestion  : — 12^  cents  is  \  of  a  dollar.     At  a  dollar  per  dozen 
the  eggs  would  cost  $  144. 


FRACTIONS  95 

3.  What  will  be  the  earnings  of  a  boy  in  44  days 
at  75  cents  per  day  ? 

4.  When  molasses  sells  at  37  J  cents  per  gallon,  how 
much  will  32  gallons  cost? 

5.  A  web  of  cloth  containing  48  yards  was  sold  at 
62^  cents  per  yard.     For  how  much  did  it  sell  ? 

6.  When  peaches  sell  at  37J  cents  per  peck,  how 
much  will  6  bushels,  or  24  pecks,  cost  ?  How  much  will 
they  cost  if  the  price  is  66%  cents  per  peck  ? 

7.  A  chest  of  choice  tea  containing  56  pounds  was 
sold  at  87J  cents  per  pound.  For  how  much  was  it 
sold? 

8.  A  man  worked  in  one  week  48  hours  at  12J  cents 
per  hour.  How  much  did  he  earn  ?  How  much  would 
he  have  earned  at  66|  cents  per  hour? 

9.  The  fare  from  Bronson  to  Oldwell  is  75  cents. 
How  much  must  be  paid  for  tickets  for  an  excursion 
party  that  numbers  60  ? 

10.  What  part  of  $1  is  25  cents?  of  $10  is  $2.50? 
of  $100  is  $25?  of  $1000  is  $250?  What  part  of 
100  is  25?  of  10  is  25?  of  1000  is  250? 

11.  What  part  of  $1  is  50  cents?  of  $10  is  $5? 
of  $100  is  $50?  of  $1000  is  $500?  What  part  of  100 
is  50?  of  1000  is  500? 

12.  What  part  of  $1  is  75  cents?  of  $10  is  $7.50? 
of  $100  is  $75?  of  $1000  is  $750?  What  part  of 
100  is  75?  of  10  is  7.5?  of  1000  is  750? 

13.  What  part  of  $1  is  12J  cents?  of  $10  is  $1.25? 
of  $100  is  $12.50?  of  $1000  is  $125?  What  part  of 
100  is  12£?  of  10  is  1.25?  of  1000  is  125? 


96  FRACTIONS 

14.  What  part  of  $100  is  $37J?  of  S100  is  $62£? 
of  $100  is  $87£?  of  $100  is  $33£?  of  $100  is  $66|? 
of  $100  is  $16f  ?  of  $100  is  $8J? 

15.  What  part  of  1000  is  375?  of  1000  is  625? 
of  1000  is  875?  of  100  is  66f  ?  of  100  is  33 J?  of  100 
is  16f  ?  of  100  is  8£?  of  1000  is  666§? 

16.  What  is  the  product  of  37|  times  48? 

Solution  :  —  Since  37£  is  f  of  100,  37J  times  48  is  f  of  100  times 
48.     100  times  48  is  4800,  and  f  of  4800  is  1800.     Therefore,  etc. 

Find  the  product  of  : 

17.  64  x  62£.  23.  48  x  66f .  29.  96  x  87£. 

18.  28  x  75.  24.  64  x  37£.  30.  84  x  16f 

19.  56  x  12£.  25.  24  x  33£.  31.  24  x  62£. 

20.  72  x  37£.  26.  32  x  75.  32.  32  x  87J. 

21.  88  x  62J.  27.  40  x  62£.  33.  52  x  75. 

22.  32  x  87J.  28.  72  x  12J.  34.  64  x  87J. 

35.  What  is  the  product  of  48  times  375? 

Suggestion  :  —  375  is  f  of  1000.  Hence  375  times  48  is  f  of 
1000  times  48. 

Find  the  product  of : 

36.  32  x  125.       41.  96  x  375.  46.  72  x  625. 

37.  24  x  375.       42.  64  x  625.  47.  40  x  875. 

38.  44  x  750.       43.  72  x  250.  48.  48  x  125. 

39.  40  x  625.       44.  88  x  125.  49.  64  x  375. 

40.  48  x  875.       45.  32  x  875.  50.  56  x  625. 

51.  What  part  of  $10  is  $3.75?  $1.25?  $6.25? 
$8.75?     $1.66|?     $3.33£?     $6.66f? 


FRACTIONS  97 

52.  How  much  will  it  cost  to  plow  32  acres  of  land 
at  13. 75  per  acre? 

Solution: — $3.75  is  }  of  $10.  At  $10  per  acre  the  plowing 
would  cost  $  320  ;  but  since  $  3.75  is  f  of  $  10,  it  will  cost  f  of  $  320, 
which  is  $  120.     Therefore,  etc. 

53.  How  much  will  72  sheep  cost  at  $  6.25  per  head  ? 

54.  A  baker  bought  88  barrels  of  flour  at  $5  3.75  per 
barrel.     How  much  did  it  all  cost  ? 

55.  How  much  will  18  cords  of  wood  cost  at  $6.66| 
per  cord? 

56.  How  much  must  be  paid  for  a  case  of  boots  con- 
taining 24  pairs  at  $3. 33 J  per  pair? 

57.  The  hats  purchased  for  a  company  consisting  of 
64  men  cost  $1.25  each.     How  much  did  they  all  cost? 

58.  A  clothier  sold  48  boys'  overcoats  at  $8.75 
apiece.     How  much  did  he  receive  for  all  of  them? 

59.  The  railroad  fare  from  Brantford  to  Hazeldon  is 
$3.75.  How  much  must  be  paid  for  tickets  for  a  party 
of  16? 

60.  The  wages  of  a  machinist  were  $3.75  per  day. 
How  much  did  he  earn  in  24  days  ? 

61.  The  porter  on  a  sleeping  car  was  paid  $37.50  per 
month  for  16  months.     How  much  did  he  earn? 

Suggestion:  — $37.50  is  §  of  $100. 

62.  The  charge  for  tuition  at  a  certain  school  was 
$62.50  per  quarter.  If  40  pupils  attended  the  school, 
to  how  much  did  the  tuition  fees  amount  per  quarter  ? 

63.  A  party  of  32  went  to  Europe  for  the  summer, 
paying  $87.50  each  for  their  passage  tickets.  How 
much  did  they  all  pay? 

MILNE    MENTAL  —  7 


98  FRACTIONS 

64.  What  part  of  $10  is  $6.25?    $16.25?    $26.25? 
Suggestion  :  — $  6.25  is  f  of  $  10,  and  $  16.25  is  If,  or  V,  of  $  10. 

65.  What  part  of  $  10  is  $  3. 75  ?    $  13. 75  ?     $  23. 75  ? 

66.  What  part  of  $10  is  $8.75?    $18.75?     $28.75? 

67.  What  part  of  $10  is  $1.25?    $11.25?    $21.25? 

68.  How  much  will  36  tons  of  hay  cost  at  $16.25  a 
ton? 

Solution  :— 116.25  is  V  of  <$  10.    At  $  10  a  ton  36  tons  will  cost 
$  360 ;  at  V  of  $  10  a  ton,  the  cost  will  be  V  of  $  360,  or  $  585. 
Therefore  36  tons  of  hay  at  $16.25  per  ton  will  cost  $585. 

69.  A  drover  bought  48  head  of  cattle  at  $18.75  a 
head.     How  much  did  they  cost? 

70.  How  much  does  a  man  earn  in  a  year  if  he  earns 
$17.50  a  week? 

71.  Find  the  cost  of  48  acres  of  land  at  $13.75  an 
acre. 

72.  How  much  does  a  man  save  in  28  weeks,  if  he 
gets  $  30  a  week  and  saves  f  of  it  ? 

73.  A  hardware  dealer  sold  56  lathes  at  $28.75  each, 
and  |  of  the  selling  price  was  gain.  How  much  did  he 
gain? 

74.  A  clothier  sold  72  suits  of  clothes  at  $21.25  a 
suit.  How  much  did  he  gain  if  they  cost  him  $15  a 
suit? 

75.  How  many  eighths  of  1000  are  there  in  1875  ?  in 
2625?  in  1125?  in  2375? 

Suggestion  :  —  Since  875  is  J  of  1000, 1875  is  1  J,  or  -1/-,  of  1000. 

76.  What  is  the  product  of  52  multiplied  by  1375? 


FRACTIONS  '..•  :■*•:  :   V  •        •-•  99 

77.  What  is  the  value  of  16*- 23782.  bf  2#k4&25*; 
of  36  xl875?  of  44  x  2125? 

78.  A  drover  bought  24  horses  at  $162.50  a  head. 
How  much  did  they  cost  ? 

79.  A  farm  of  48  acres  was  sold  at  $  375  per  acre. 
How  much  was  received  for  it? 

80.  How  much  does  a  man  earn,  in  16  years  whose 
salary  is  $1875  per  year? 

81.  A  mining  company  shipped  36  tons  of  ore  per 
day.  What  was  the  value  of  the  output,  if  it  was  sold 
for  $175  a  ton? 

82.  If  a  steamer  averages  375  miles  a  day,  how  far 
can  it  go  in  16  days  ? 

83.  If  a  farmer  can  raise  125  bushels  of  potatoes  on 
one  acre,  how  many  bushels  can  he  raise  on  29  acres  ? 

84.  How  much  must  be  paid  for  48  shares  of  bank 
stock  at  $36.66|  per  share? 

85.  A  man  paid  $38.75  per  month  rent.  How  much 
was  that  per  year? 

39.  1.  How  many  books  at  75  cents  each  can  be 
bought  for  $9? 

2.  A  boy  working  for  $1.37 \  per  day  earned  in  a 
certain  time  $33.     How  many  days  did  he  work  ? 

3.  How  many  times  is  133J  contained  in  800?  in 
1200?  in  2000?  in  3600? 

4.  At  $  2.87^  a  cord,  how  much  wood  can  be  bought 
for  $230? 

Suggestion  :  —  $ 2.87 1  is  |2|,  or  $-2/. 


190  FRACTIONS 

^5.  ■Howiiaanytons  of  coal  at  $4.75  per  ton  can  be 
bought  for  $  190  ? 

6.  A  man  earns  $3.75  a  day.     How  long  will  it 
take  him  to  earn  $  60  ? 

7.  At  $16.25  a  ton,  how  many  tons  of  hay  can  be 
bought  for  $91? 

Suggestion  :  —  $  16.25  is  ^  of  $  10. 

8.  If  a  man  pays  $  2300  for  land  at  $28.75  per  acre, 
how  many  acres  does  he  buy  ? 

9.  A   certain   number  multiplied  by  875  gives   a 
product  of  28,000.     What  is  the  number  ? 

Suggestion:  —  If  the  multiplier  had  been  1000,  the  number 
would  have  been  28;  but  875  is  |  of  1000,  therefore  28  is  J  of  the 
number. 

10.  At  $13.75  per  week  how  long  will  it  take  a 
salesman  to  earn  $  880  ? 

11.  An  ocean  steamer  that  averages  375  miles  a  day 
makes  a  voyage  of  6000  miles.     How  long  does  it  take  ? 

12.  A  vessel  pays  $1.25  toll  per  ton  for  passing 
through  the  Suez  Canal.  What  is  her  tonnage  if  the 
toll  charges  are  $4500? 

13.  At  $6.75  per  yard,  how  many  yards  of  broad- 
cloth can  be  bought  for  $150? 

14.  If  John  can  walk  2$  miles  per  hour,  how  long 
will  it  take  him  to  go  69  miles? 

15.  If  a  gallon  of  varnish  costs  $  If,  how  many  gal- 
lons can  be  bought  for  $  130  ? 

16.  A  coal  dealer  sold  f  of  his  coal  at  $3. 87  J  a  ton 
and  realized  $  930.     How  many  tons  had  he  ? 


FRACTIONS  •  ,;  :    v  •        '  '1:01 

17.  Shoes  bought  at  $2.62f  •'Jpeft?'  pair  aVe  :sbld '  at' 
$3.37^.  If  $12  is  the  gain  on  one  case  of  such  shoes, 
how  many  pairs  were  there  in  each  case  ? 

18.  How  many  times  is  121.25  contained  in  $  850  ? 
in  $1020?  in  $1700? 

19.  A  wagon  load  of  potatoes  sold  at  62J  cents  a 
bushel  brought  $35.  How  many  bushels  of  potatoes 
were  there  in  the  wagon? 

20.  How  many  days  must  a  man  work  at  $1.87 J  a 
day  to  earn  $  60  ? 

21.  When  gloves  are  $1.37 J  a  pair,  how  many  pairs 
can  be  bought  for  $110  ? 

22.  Some  cattle  were  bought  at  $31.25  a  head. 
How  many  were  there,  if  they  all  cost  $  1000  ? 

23.  A  train  runs  36^  miles  per  hour.  In  how  many 
hours  can  it  run  580  miles  ? 

24.  What  is  the  value  of  6300 -h26£?  of  9300 -38f? 
of  9100-*- 1621? 

25.  A  man  expended  $800  for  hay  at  $16.66|  a  ton. 
How  many  tons  did  he  buy? 

26.  A  man  pays  a  debt  of  $740  at  the  rate  of  $46.25 
per  month.     In  what  time  does  he  pay  the  debt  ? 

27.  A  man  buys  land  at  $18.75  per  acre  and  sells  it 
at  $36.25  per  acre.  How  many  acres  must  he  sell  to 
gain  $700? 

28.  How  many  yards  of  sheeting  at  18|  cents  per 
yard  can  be  bought  for  $  15  ? 

29.  A  merchant  sold  umbrellas  at  $1.75  each.  How 
many  were  there  if  he  sold  all  he  had  and  received  for 
them  $56? 


102  :  :       ..   FRACTIONS 

:  40.*  1.  %Twd  m&r'did  a  piece  of  work  for  $72.  One 
worked  11  days,  and  the  other  7  days.  If  their  daily 
wages  were  the  same,  how  much  should  each  receive  ? 

2.  Two  boys  bought  48  marbles  for  8  cents.  One 
paid  5  cents,  and  the  other  3  cents.  How  many  mar- 
bles should  each  receive  ? 

3.  A  man  bought  an  equal  number  of  sheep  and 
pigs  for  $130.  The  sheep  cost  $5  each,  and  the  pigs 
$  8  each.  How  much  did  he  pay  for  the  sheep,  and 
how  much  for  the  pigs? 

4.  Two  men,  120  miles  apart,  approach  each  other 
at  the  rates  of  3  miles  and  5  miles  per  hour  respec- 
tively. When  they  meet,  how  many  hours  will  each 
have  traveled?     How  far  will  each  have  traveled? 

5.  Divide  the  number  140  into  2  parts  that  shall  be 
to  each  other  as  4  to  3. 

Suggestion  :  —  In  every  7  units  of  the  given  number  4  units 
belong  in  one  part  and  3  in  the  other. 

6.  One  drover  had  14  horses,  and  another  11.  A 
farmer  charged  them  $  37|-  for  keeping  the  animals. 
How  much  should  each  drover  pay  ? 

7.  A  and  B  plowed  a  field  for  1 30.  A  worked  7 
days,  and  B  5  days.     How  much  should  each  receive? 

8.  A  teacher  had  an  equal  number  of  boys  and  girls 
in  her  class.  She  gave  4  questions  to  each  boy,  and 
3  to  each  girl.  In  all  she  gave  280  questions.  How 
many  pupils  were  there  in  the  class  ? 

9.  Two  men  hire  a  boat  for  $21.  The  first  uses  it  16 
days  and  the  second  26  days.  How  much  should  each 
pay? 


FRACTIONS  103 

10.  A  man  paid  $52  for  the  pasture  of  8  horses  and 
14  cows.  How  much  did  the  pasturage  of  the  horses 
cost,  and  how  much  the  pasturage  of  the  cows,  if  2 
horses  eat  as  much  as  3  cows? 

11.  Two  numbers  are  to  each  other  as  7  to  9,  and 
their  sum  is  80.     What  are  the  numbers  ? 

12.  A  and  B  agree  to  do  a  piece  of  work  for  $130. 
A  sends  5  men,  and  B  12  boys.  How  much  should 
each  receive  if  3  boys  can  do  as  much  work  as  2  men  ? 

13.  One  contractor  has  6  men  on  a  piece  of  work  for 
4  days,  and  another  contractor  has  on  the  same  work  5 
men  for  6  days.  They  receive  together  for  the  work 
$108.     How  much  belongs  to  each? 

14.  Three  men  together  bought  600  bushels  of  pota- 
toes. The  first  paid  ^  of  the  cost,  the  second  ^,  and  the 
third  paid  the  remainder.  How  many  bushels  should 
each  receive  ? 

15.  Three  gangs  of  workmen  build  a  boat  for  $650; 
the  first  gang  of  6  men  works  5  days,  the  second  of  5 
men  works  8  days,  and  the  third  of  10  men  works  6 
days.     How  much  should  each  gang  get? 

16.  A  piece  of  work  is  done  by  4  men  and  7  boys  in 
4  days  for  $68.  If  2  men  can  do  as  much  as  5  boys, 
what  are  the  daily  earnings  of  a  man  and  of  a  boy? 

17.  Divide  $  280  among  A,  B,  and  C,  so  that  A  shall 
receive  $  2  as  often  as  B  receives  $  5,  and  C$7. 

18.  Three  boys  together  bought  48  apples,  the  first 
paying  4  cents,  the  second  5  cents,  and  the  third  7 
cents.     How  many  apples  should  each  receive  ? 


104  FRACTIONS 

19.  If  3  oranges  cost  as  much  as  5  apples,  and  a 
dozen  of  each  cost  together  96  cents,  how  much  do  they 
cost  apiece  ? 

20.  Two  men  bought  a  horse  for  $  100,  of  which  the 
first  paid  $60.  They  sold  it  for  f  150.  How  much  of 
the  selling  price  should  each  receive  ? 

21.  Into  a  pasture  that  was  rented  for  172,  A  put 
4  horses,  B  9  cows,  and  C  21  sheep.  How  much  should 
each  pay  for  his  share  of  the  rent,  if  2  horses  eat  as 
ruuch  as  3  cows,  and  1  cow  as  much  as  7  sheep  ? 

22.  Two  partners  together  gained  $850.  The  first 
put  into  the  business  $  250  for  4  months,  and  the  second 
$  350  for  2  months.     Find  each  man's  share  of  the  gain. 

Suggestion  :  —  The  investment  of  the  first  was  the  same  as 
$  1000  for  1  month,  and  the  investment  of  the  second  the  same  as 
$700  for  1  month. 

41.  1.  A  lady  bought  a  certain  number  of  yards  of 
lace  at  8  cents  a  yard.  If  she  had  paid  12  cents  a  yard, 
it  would  have  cost  48  cents  more.  How  many  yards 
did  she  buy  ? 

Solution  :  —  Paying  12  cents  a  yard  instead  of  8  cents  makes 
the  cost  4  cents  more  for  each  yard.  Since  the  total  difference  in 
the  cost  was  48  cents,  she  must  have  bought  as  many  yards  as  4 
cents  are  contained  times  in  48  cents,  or  12  yards.     Therefore,  etc. 

2.  A  man  gave  some  children  5  cents  each.  If  he 
had  given  them  10  cents  each,  it  would  have  taken  50 
cents  more.     How  many  children  were  there? 

3.  A  man  bought  some  calves  at  $5  each  and  had 
$  45  left.  If  he  had  bought  as  many  hogs  at  $  7  each, 
he  would  have  had  only  $  5  left.  How  many  calves  did 
he  buy? 


FRACTIONS  105 

4.  A  teacher  took  some  pupils  on  an  excursion,  and 
after  expending  15  cents  for  each  pupil,  she  found  that 
she  had  $  2  left.  If  she  had  expended  20  cents  for  each, 
she  would  have  had  only  $  1  left.  How  many  pupils 
were  there? 

5.  If  I  had  paid  5  cents  each  instead  of  3  cents  for 
a  certain  number  of  oranges,  they  would  have  cost  24 
cents  more  than  they  did  cost.     How  many  did  I  buy  ? 

6.  A  lady  had  money  enough  to  pay  15  cents  a  yard 
for  some  ribbon,  and  have  50  cents  left.  If  she  had 
paid  25  cents  a  yard  for  it,  she  would  have  needed  50 
cents  more.  How  many  yards  were  there,  and  how 
much  money  had  she  ? 

7.  A  man  divided  45  excursion  tickets  among  an 
equal  number  of  boys  and  girls,  giving  to  each  boy  4, 
and  to  each  girl  5.     How  many  children  were  there  ? 

8.  A  farmer  sold  an  equal  number  of  sheep  and 
pigs  for  $100.  How  many  were  there  of  each,  if  he 
received  $4  each  for  the  sheep  and  $6  each  for  the 
pigs? 

9.  Two  men  together  earn  $60  in  a  certain  time. 
How  much  should  each  receive,  if  they  are  paid  at  the 
rate  of  $1J  and  $2J  a  day  respectively? 

10.  If  a  drover  pays  $40  a  head  for  some  cattle,  he 
will  have  $20  left;  but  if  he  pays  $50  a  head,  he  will 
need  $100  more  with  which  to  pay  for  them.  How 
many  are  there  ? 

11.  I  bought  some  lemons  at  3  cents  each  and  twice 
as  many  oranges  at  4  cents  each.  They  all  cost  $1.10. 
How  many  were  there  of  each  ? 


106  FRACTIONS 

42.  1.  Mary  can  make  a  dress  in  3^  days.  What 
part  of  the  work  can  she  do  in  J  day?  in  1  day? 

2.  A,  B,  and  C  can  dig  a  trench  in  2|  days;  B  alone 
can  do  it  in  8  days ;  B  and  C  can  do  it  in  4|  days.  In 
what  time  can  A  and  C  each  do  it? 

3.  If  3  men  can  do  as  much  work  as  5  boys,  and  if  5 
men  can  do  a  piece  of  work  in  6  days,  how  long  will 
it  take  5  men  and  10  boys  to  do  the  work? 

4.  A  can  plow  a  field  in  4  days,  and  B  can  do  it  in 
6  days.  How  long  will  it  take  A  to  plow  the  field,  if 
B  works  with  him  half  of  the  time  ? 

5.  A  can  mow  J  of  a  field  while  B  mows  |  of  it. 
If  they  can  together  mow  it  in  3|  days,  in  what  time 
can  each  alone  do  the  work? 

6.  A  can  make  a  coat  in  3  days,  and  B  can  make  4 
coats  in  10  days.  How  long  will  it  take  them  to  make 
11  coats  together? 

7.  A  and  B  can  build  a  wall  in  3  days,  A  and  C  in 
6  days,  and  B  and  C  in  2f  days.  In  what  time  can 
each  alone,  and  all  together,  do  the  work? 

Suggestion: — A  and  B  can  do  J  of  the  work  in  1  day;  A  and 
C  can  do  |  of  the  work  in  1  day;  B  and  C  can  do  ^  °f  tne  work 
in  1  day.  Hence,  twice  what  A,  B,  and  C  can  do  in  one  day  is  \\ 
of  the  work. 

8.  A  and  B  can  do  a  piece  of  work  in  4  days,  A  and 
C  in  6  days,  and  B  and  C  in  8  days.  How  long  will  it 
take  each  one  to  do  the  work? 

9.  A  and  B  can  row  a  distance  in  4  hours.  B  can 
do  it  alone  in  9  hours.  After  they  have  rowed  together 
3  hours  A  finishes.     How  long  does  it  take  him? 


FRACTIONS  107 

43.  1.  The  sum  of  two  numbers  is  30,  and  their 
difference  is  8.     What  are  the  numbers  ? 

Solution  :  —  Since  one  number  is  8  more  than  the  other,  their 
sum,  30,  is  8  more  than  twice  the  less.  Hence  22  is  twice  the  less ; 
and  11  is  the  less,  and  19  the  greater.     Therefore,  etc. 

2.  Two  girls  have  together  43  buttons,  of  which  one 
has  9  more  than  the  other.     How  many  has  each? 

3.  The  sum  of  two  numbers  is  50;  their  difference 
is  12.     Find  the  numbers. 

4.  Harry  and  his  brother  earned  $1,  of  which  Harry 
earned  30  cents  more  than  his  brother.  How  much  did 
each  earn  ? 

5.  A  bushel  of  wheat  cost  20  cents  more  than  a 
bushel  of  rye,  and  a  bushel  T)f  each  cost  together  $  If. 
How  much  did  each  cost  per  bushel  ? 

6.  Louis  and  his  brother  had  each  the  same  number 
of  marbles.  Louis  bought  25  more,  and  then  they  had 
together  85.     How  many  had  each  at  first  ? 

7.  Two  farmers  had  each  the  same  number  of  sheep. 
After  one  sold  25,  and  the  other  35,  together  they  had 
left  100.     How  many  had  each  at  first? 

8.  Two  boys  each  bought  a  bicycle  at  the  same  price. 
One  sold  his  for  $  10  less  than  cost,  and  the  other  sold 
his  for  $8  less  than  cost.  The  sum  received  for  both 
was  $62.     How  much  did  they  pay  for  them? 

9.  If  |  the  sum  of  two  numbers  is  39,  and  J  of  their 
difference  is  6,  what  are  the  numbers  ? 

10.  If  ^  of  a  number  is  increased  by  10,  4  times  the 
sum  will  be  §  of  150.     What  is  the  number? 


108  FRACTIONS 

11.  If  |  of  a  certain  number  is  multiplied  by  4,  |  of 
the  product  is  50.     What  is  the  number? 

12.  A  and  B  dug  in  one  day  103  bushels  of  potatoes. 
How  many  bushels  did  each  dig,  if  A  dug  12  bushels 
more  than  |  of  what  B  dug  ? 

13.  Mr.  Brown  is  8  years  more  than  twice  as  old  as 
his  son,  and  the  difference  in  their  ages  is  22  years. 
How  old  is  each? 

14.  After  paying  $18  more  than  |  of  my  money  for 
an  overcoat,  I  have  f  of  it  left.  How  much  did  the 
overcoat  cost  ? 

15.  A  farmer  sold  20  acres  less  than  jj-  of  his  land, 
and  received  $4000  for  the  remainder  at  $50  per  acre. 
How  many  acres  had  he  at  first? 

16.  A  has  2^  times  as  many  sheep  as  B  ;  but  if  he 
sells  25  of  his  sheep  to  B,  they  will  have  the  same  num- 
ber.    How  many  has  each? 

17.  Mary's  age  is  f  of  her  mother's  age,  and  in  3 
years  the  sum  of  their  ages  will  be  50  years.  How  old 
is  each? 

18.  A  boat  goes  down  stream  a  certain  distance ;  it 
then  turns,  and  goes  up  stream  12  miles  more  than  f  of 
the  distance  it  sailed  down.  If  the  entire  distance  sailed 
was  20  miles,  how  far  did  it  sail  down  stream? 

19.  If  you  should  multiply  a  certain  number  by  5, 
subtract  16  from  the  product,  and  divide  the  remainder 
by  2,  the  quotient  would  be  72.     What  is  the  number? 

20.  A  coat  and  a  vest  cost  $27.  ^  the  cost  of  the 
coat,  plus  $2,  equals  the  cost  of  the  vest.  How  much 
does  each  cost  ? 


DENOMINATE   NUMBERS 


44.  1.  How  many  inches  are  there  in  1  foot?  in  2 
feet?  in  5  feet?  in  7  feet?  in  11  feet? 

2.  How  many  inches  are  there  in  1  foot  8  inches? 
in  2  feet  6  inches  ?  in  1  yard  ?  in  1  yard  2  feet  ? 

3.  How  many  feet  are  there  in  24  inches?  in  60 
inches  ?  in  84  inches  ?  in  96  inches  ? 

4.  How  many  yards  are  there  in  9  feet?  in  15  feet? 
in  144  inches  ?  in  108  inches  ? 

5.  How  many  yards  are  there  in  2  rods  ?  how  many 
feet  ?  How  many  feet  are  there  in  4  rods  ?  how  many 
yards? 

6.  How  many  yards  are  there  in  1  rod?  how  many 
feet  ?  How  many  feet  are  there  in  5  rods  ?  how  many 
yards  ? 

7.  When  I  pay  90  cents  a  yard  for  carpet  27  inches 
wide,  how  much  should  I  pay  for  carpet  of  the  same 
quality  1  yard  wide? 

8.  If  a  piece  of  ribbon  1  foot  8  inches  long  costs 
25  cents,  how  much  should  be  paid  for  a  piece  of  the 
same  kind  1  yard  1  foot  6  inches  long? 

9.  What  will  be  the  cost  of  a  piece  of  silk  velvet 
60  inches  long  at  $  6  a  yard  ? 

109 


110  DENOMINATE   NUMBERS 

10.  What  will  a  piece  of  manilla  rope  240  inches 
long  cost  at  18  cents  a  yard? 

11.  If  a  man  goes  1  rod  in  5  steps,  how  many 
steps  will  he  take  in  going  1  mile  ? 

12.  If  I  pay  48  cents  for  2  feet  8  inches  of  lead  pipe, 
how  much  must  I  pay  for  a  piece  of  the  same  kind  3 
feet  9  inches  long  ? 

13.  A  horse  runs  5  furlongs  in  1  minute  25  seconds. 
At  that  rate  how  long  will  it  take  him  to  run  1  mile  ? 

14.  How  much  must  be  paid  for  a  piece  of  mahogany 
molding  5  yards  2  feet  8  inches  long,  at  6  cents  a 
foot? 

15.  A  man  who  steps  30  inches  at  each  step  wishes 
to  measure  a  distance  of  100  yards.  How  many  steps 
must  he  take  ? 

16.  How  much  will  50  yards  of  garden  hose  cost  at 
8  cents  a  foot  ? 

45.  1.  How  many  square  inches  are  there  in  2 
square  feet?  in  3  square  feet?  in  10  square  feet? 

2.  In  5  square  yards  how  many  square  feet  are 
there?  in  8  square  yards?  in  10  square  yards? 

3.  In  2  square  rods  how  many  square  yards  are 
there?  how  many  square  feet? 

4.  A  farmer  raises  100  bushels  of  potatoes  to  the 
acre.  How  many  bushels  should  he  get  from  a  field 
containing  240  square  rods? 

5.  A  field  of  5  acres  is  divided  into  lots  each  con- 
taining 100  square  rods.     How  many  lots  are  there  ? 


DENOMINATE   NUMBERS  HI 

6.  At  10  cents  a  square  foot,  what  will  be  the  cost 
of  a  piece  of  zinc  6  feet  square  ? 

Suggestion  :  —  The  area  of  a  square  or  oblong  is  equal  to  the 
product  of  the  two  numbers  expressing  its  dimensions.  These 
numbers  must  express  units  of  the  same  name,  and  the  result  will 
be  in  square  units  of  that  name. 

Thus  the  area  of  an  oblong  3  feet  long  and  2  feet  wide  is  6 
square  feet. 

7.  How  much  must  be  paid  for  a  mahogany  plank 
12  feet  long  and  1^  feet  wide  at  20  cents  a  square  foot  ? 

8.  At  20  cents  a  square  yard,  how  much  must  be 
paid  for  sodding  a  lawn  5  yards  long  and  4  yards  wide  ? 

9.  How  many  acres  are  there  in  a   field   80   rods 
long  and  20  rods  wide? 

10.  At  20  cents  a  square  foot,  how  much  must  be 
paid  for  a  sheet  of  plate  glass  10  feet  long  and  6  feet 
wide? 

11.  How  much  will  it  cost  to  plaster  a  ceiling  18 
feet  square,  at  25  cents  a  square  yard? 

12.  A  lot  10  rods  long  contains  half  an  acre.  How 
wide  is  it? 

13.  A  surveyor's  chain  is  4  rods  long.  How  many 
acres  are  there  in  a  field  10  chains  long  and  5  chains 
wide? 

14.  How  many  square  feet  are  there  in  3  boards, 
each  20  inches  wide  and  16  feet  long? 

15.  What  is  the  difference  between  a  surface  5  yards 
square  and  one  containing  5  square  yards?  between 
4  square  feet  and  4  feet  square  ? 


112  DENOMINATE  NUMBERS 

46.  1.  How  many  cubic  inches  are  there  in  2  cubic 
feet  ?  in  10  cubic  feet  ? 

2.  How  many  cubic  feet  are  there  in  2  cubic  yards  ? 
in  5  cubic  yards  ?  in  2  cords  ? 

3.  If  a  man  gets  3  cents  a  cubic  foot  for  digging  a 
cellar,  how  much  does  he  get  for  digging  3  cubic  yards  ? 

4.  How  many  cords  are  there  in  a  pile  of  wood  16 
feet  long,  8  feet  high,  and  4  feet  wide  ? 

Suggestion.  —  The  volume  of  any  rectangular  solid  is  equal  to 
the  product  of  the  three  numbers  representing  its  dimensions. 
The  numbers  must  express  units  of  the  same  name,  and  the  re- 
sult will  be  in  solid  units  of  that  name. 

Thus,  the  volume  of  a  solid  whose  dimensions  are  2  feet,  3  feet, 
and  4  feet  is  24  cubic  or  solid  feet. 

5.  What  is  the  value  of  a  block  of  granite  6  feet 
square  and  5  feet  high  at  50  cents  a  cubic  foot  ? 

6.  If  it  costs  $  72  to  excavate  a  cellar  6  yards  square, 
at  $  1  a  cubic  yard,  how  deep  is  the  cellar? 

7.  How  many  cords  of  wood  can  be  placed  in  a 
space  8  feet  each  way? 

8.  A  bushel  is  almost  exactly  1J  cubic  feet.  How 
many  bushels  will  a  bin  hold  that  is  8  feet  long,  6  feet 
wide,  and  5  feet  deep  ? 

9.  What  must  be  the  capacity  in  cubic  feet,  of  a  bin 
that  will  hold  480  bushels  of  wheat  ?  Give  the  dimen- 
sions of  several  such  bins. 

10.  A  square  cellar  that  is  6  feet  deep  has  a  capacity 
of  800  cubic  yards.     What  are  its  other  dimensions  ? 

11.  A  vat  25  feet  long  and  20  feet  wide  is  full  of 
water.  How  many  cubic  feet  must  be  drawn  off  to 
sink  the  surface  6  feet  ? 


DENOMINATE   NUMBERS  113 

12.  A  brick  is  usually  8  inches  long,  4  inches  wide, 
and  2  inches  thick.  How  many  such  bricks  are  there 
in  a  pile  whose  dimensions  are  8  feet,  4  feet,  and  2  feet  ? 

13.  How  many  cubical  blocks  2  inches  on  an  edge 
can  be  put  into  a  box  8  inches  on  each  edge  ? 

14.  A  cubic  foot  of  water  weighs  62^  pounds.  What 
weight  of  water  would  be  contained  in  a  cistern  5  feet 
square  and  4  feet  deep  ? 

15.  What  will  be  the  cost,  at  25  cents  a  cubic  foot,  of 
a  piece  of  marble  16  inches  square  and  27  feet  long  ? 

16.  A  block  of  stone  12  feet  long  and  8  feet  wide, 
bought  at  50  cents  a  cubic  foot,  cost  $288.  How  thick 
was  it  ? 

47.  1.  How  many  gills  are  there  in  1  pint?  in  1 
quart  ?  in  1  gallon  ?  in  2  quarts  1  pint  ? 

2.  How  many  quarts  are  there  in  2  gallons?  in  3 
gallons  3  quarts  ?  in  4  gallons  1  quart  ? 

3.  How  many  pints  are  there  in  1  gallon  3  quarts  ? 
in  2  gallons  1  quart  1  pint  ?  in  3  gallons  3  quarts  1 
pint  ?  in  1  gallon  2  quarts  1  pint  ? 

4.  What  part  of  a  gallon  is  1  quart  1  pint?  2 
quarts  1  pint  3  gills  ?  3  quarts  2  gills  ? 

5.  How  many  times  1\  pints  are  2|  gallons  ?  How 
many  times  are  3  pints  3  gills  contained  in  3|  quarts  ? 

6.  A  milkman  buys  milk  at  the  rate  of  16  cents  a 
gallon  and  sells  it  at  5  cents  a  pint.  How  much  must 
he  sell  to  gain  $6? 

7.  A  grocer  buys  40  gallons  of  vinegar  at  20  cents 
a  gallon  and  retails  it  at  10  cents  a  quart.  How  much 
does  he  gain  ? 

MILNE    MENTAL  —  8 


114  DENOMINATE   NUMBERS 

8.  A  grocer  bought  30  gallons  of  sirup  for  $24 
and  retailed  it  at  25  cents  a  quart.  How  much  did 
he  gain? 

9.  If  a  gallon  of  alcohol  sells  for  f>l£,  how  much 
must  be  paid  for  1  quart  1  pint  ?  for  3  quarts  1  pint  ? 

10.  How  much  was  received  for  2  gallons  of  cream 
sold  at  5  cents  a  gill  ? 

11.  If  8  vessels  of  equal  size  contain  3  gallons,  how 
much  does  each  vessel  contain  ? 

12.  How  many  times  can  a  lamp  holding  1  pint  2 
gills  be  filled  from  a  can  holding  1 J  gallons  ? 

13.  I  pay  $2-|  in  14  days  for  milk  at  10  cents  a 
quart.     How  much  do  I  buy  daily  ? 

14.  How  much  must  be  paid  for  3  pints  2  gills  of 
cologne  at  $  8  per  gallon  ? 

48.     1.    How  many  quarts  are  there  in  a  peck?   how 
many  pints  ?     How  many  quarts  are  there  in  a  bushel  ? 

2.  In  96  quarts  how  many  pecks  are  there?  how 
many  bushels  ? 

3.  If  1  bushel  of  chestnuts  is  bought  for  $  1-|,  and 
sold  at  10  cents  a  quart,  how  much  is  gained  ? 

4.  I  bought  J  bushel  of  cranberries  for  $1^  and 
sold  them  at  10  a  quart.     How  much  was  gained  ? 

5.  My  chickens  eat  1  quart  1  pint  of  corn  daily. 
How  long  will  5  pecks  last  them  ? 

6.  A  man  picked  3  pecks  of  blueberries  and  sold 
them  at  10  cents  a  quart.  How  much  did  he  get  for 
them? 


DENOMINATE   NUMBERS  H5 

7.  At  30  cents  a  peck,  how  many  bushels  of  apples 
can  be  bought  for  $12? 

8.  What  will  be  the  cost  of  1  bushel  3  quarts  1  pint 
of  beans  at  $1.28  a  bushel  ? 

9.  What  part  of  a  bushel  is  1  peck  3  quarts?  3 
pecks  4  quarts  ?     2  pecks  6  quarts  ? 

10.  If  5  pints  of  chestnuts  cost  30  cents,  how  much 
will  3  pecks  cost  ? 

11.  A  farmer  sold  1  bushel  3  pecks  4  quarts  of  clover 
seed  at  $  8  a  bushel.     How  much  did  he  get  for  it  ? 

12.  A  man  sold  1  bushel  1  peck  5  quarts  of  cherries 
at  64  cents  a  bushel.     How  much  did  he  get  for  them  ? 

13.  I  paid  $1.60  per  bushel  for  peanuts,  and  sold 
them  at  5  cents  for  \  pint.  How  much  did  I  gain  on 
each  peck? 

14.  At  $1  per  bushel,  how  much  will  3  bushels  3 
pecks  4  quarts  of  potatoes  cost? 

49.  1.  How  many  ounces  are  there  in  1  pound  Avoir- 
dupois ?  in  2  pounds  ?  in  5  pounds  ? 

2.  How  many  pounds  are  there  in  32  ounces  ?  in 
48  ounces  ?  in  80  ounces  ?  in  64  ounces  ? 

3.  How  many  ounces  are  there  in  1|  pounds  ?  in  2J 
pounds  ?  in  5J  pounds  ?  in  4|  pounds  ? 

4.  How  many  pounds  are  there  in  1J  hundred- 
weight ?  in  2^  hundredweight  ?  in  3  hundredweight  75 
pounds  ?  in  5  hundredweight  67  pounds  ? 

5.  Change  3  pounds  12  ounces  to  ounces ;  4  pounds 
5  ounces ;  5  pounds  6  ounces  ;  6  pounds  4  ounces. 


116  DENOMINATE   NUMBERS 

6.  How  many  hundredweight  are  there  in  1 J  tons  ? 
in  1£  tons  ?  in  2|  tons  ?  in  3f  tons  ? 

7.  At  $15  a  ton,  how  much  must  be  paid  for  800 
pounds  of  hay  ?  for  2800  pounds  ?  for  3000  pounds  ? 

8.  The  coal  in  a  wagon  weighed  2300  pounds. 
How  much  was  it  worth  at  $  4  per  ton  ? 

9.  Five  boys  share  equally  2  pounds  8  ounces  of 
candy.     How  much  does  each  receive  ? 

10.  What  will  be  the  cost  of  3  pounds  10  ounces  of 
butter  at  24  cents  a  pound  ? 

11.  What  part  of  1  hundredweight  are  64  pounds? 
40  pounds  ?  96  pounds  ?  70  pounds  ? 

12.  A  granite   block  weighed   3   tons   16   hundred- 
weight.    How  much  did  it  cost  at  $5  per  ton? 

13.  If  4  marble  blocks  of  equal  size  weigh  together  1 
ton  16  hundredweight,  what  is  the  weight  of  each  ? 

14.  I  paid  60  cents  for  3  pounds  12  ounces  of  beef. 
How  much  should  be  paid  for  2  pounds  9  ounces  ? 

50.   1.    How  many  ounces  are  there  in  1  pound  Troy 
weight  ?  in  2  pounds  ?  in  3^  pounds  ?  in  2|  pounds  ? 

2.  How  many  grains  are  there  in  2  pennyweights? 
in  5  pennyweights  ?  in  3J  pennyweights  ?  in  2|  penny- 
weights ?  in  4^  pennyweights  ? 

3.  Change  2  ounces  to  pennyweights ;  3^  ounces ; 
4|  ounces ;  1  pound  ;  1  pound  4  ounces. 

4.  How  many  grains  are  there  in  1  ounce?  in  1 
pound  ?  in  2  pounds  2  ounces  ? 

5.  How  much  will  1  pound  of  gold  cost  at  60  cents 
a  pennyweight? 


DENOMINATE   NUMBERS  117 

6.  A  gold  watch  case  weighing  2J  ounces  was  sold 
at  50  cents  a  pennyweight.  How  much  was  received 
for  it? 

7.  What  is  the  value  of  1  ounce  of  metallic  cerium 
at  50  cents  a  grain  ? 

8.  The  price  of  the  rare  metal  gallium  is  $25  for  1J 
grains.  At  that  rate,  how  much  will  1  pennyweight 
of  it  cost  ? 

9.  What  part  of  a  pound  is  1  ounce  4  pennyweights? 
What  part  of  an  ounce  are  96  grains? 

10.  If  a  dozen  spoons  of  equal  weight  are  made  from 
3  pounds  6  ounces  of  silver,  how  much  does  each  spoon 
weigh  ? 

11.  Pure  gold  is  worth  about  4  cents  a  grain.  At 
that  rate,  how  much  will  1  pennyweight  cost?  1 
ounce  ? 

51.  1.  How  many  days  are  there  in  3  weeks?  in  4 
weeks  ?  in  a  fortnight  ? 

2.  In  an  ordinary  year  there  are  365  days.  How 
man}'  weeks  are  there? 

3.  The  year  1890  began  on  Wednesday.  On  what 
day  did  1891  begin? 

4.  What  is  the  greatest  number  of  Sundays  that 
can  occur  in  a  year? 

5.  The  year  1892  began  on  Friday.  On  what  day 
did  1893  begin?  1894?  1895? 

6.  Mention  the  months  that  have  31  days.  Mention 
those  that  have  30  days. 


118  DENOMINATE   NUMBERS 

7.  A  railroad  train  goes  a  mile  in  1  minute  20 
seconds.     What  is  the  rate  per  hour? 

8.  The  length  of  a  day  is  equal  to  twice  the  time 
at  which  the  sun  sets.  How  long  is  the  day  when  the 
sun  sets  at  15  minutes  to  7  o'clock  ? 

9.  The  length  of  the  night  is  equal  to  twice  the 
time  at  which  the  sun  rises.  How  long  is  the  night 
when  the  sun  rises  at  10  minutes  to  5  o'clock  ?  How 
long  is  the  day? 

10.  Which  of  the  following  years  are  leap  years: 
1850,1860,1868,1890,1900? 

11.  Which  are  the  winter  months  in  the  northern 
hemisphere  ?  in  the  southern  hemisphere  ? 

12.  How  many  days  are  there  from  April  1  to  July 
4?  from  the  beginning  of  winter  to  Christmas? 

13.  How  many  days  are  there  in  January,  February, 
and  March,  1896? 

14.  A  man  walked  13  miles  in  4  hours  20  minutes. 
What  was  his  rate  per  hour? 

15.  A  horse  runs  f  of  a  mile  in  1  minute  40  seconds. 
In  what  time  will  he  run  a  mile  at  that  rate  ? 

16.  At  what  time  between  1850  and  1950  does  it 
happen  that  8  years  elapse  between  leap  years? 

17.  A  boy  goes  to  bed  at  half  past  eight  and  rises  at 
20  minutes  to  seven.     How  long  is  he  in  bed? 

18.  If  a  year  begins  on  Sunday,  on  what  day  of  the 
week  does  it  end  if  it  is  an  ordinary  year?  if  it  is  a 
leap  year? 


DENOMINATE   NUMBERS  119 

52.  1.  How  many  farthings  are  there  in  a  penny? 
in  2  pence?  in  5  pence?  in  12  pence? 

2.  How  many  pence  are  there  in  12  farthings?  in 
20  farthings?  in  36  farthings? 

3.  How  many  pence  are  there  in  1  shilling?  in  3 
shillings?  in  5  shillings? 

4.  How  many  farthings  are  there  in  1  shilling?  in 
1  shilling  6  pence  ?  in  1  shilling  9  pence  ? 

5.  How  many  pence  are  there  in  1  shilling  3  pence? 
in  2  shillings  9  pence?  in  3  shillings  6  pence? 

6.  Reduce  36  pence  to  shillings ;  60  pence ;  70 
pence ;  100  pence ;  120  pence. 

7.  How  many  shillings  are  there  in  1  pound?  how 
many  pence  ?  How  many  shillings  are  there  in  2  pounds 
10  shillings  ? 

8.  How  many  pounds  will  60  bushels  of  apples  cost 
at  3  shillings  per  bushel? 

9.  How  much  will  40  yards  of  ribbon  cost  at  1 
shilling  3  pence  a  yard? 

10.  At  6  pence  each  how  much  will  40  melons  cost? 

11.  What  part  of  a  pound  are  2  shillings  6  pence? 
7  shillings  6  pence?  12  shillings  6  pence? 

12.  A  shilling  is  worth  about  24  cents.  What  is  the 
value  in  United  States  money  of  1  pound? 

13.  A  man  expended  1  pound  10  shillings  for  oats 
at  1  shilling  6  pence  per  bushel.  How  many  bushels 
did  he  buy? 

14.  How  much  does  a  man  earn  in  6  days  who  gets 
5  shillings  8  pence  per  day  ?  How  much  would  that  be 
in  United  States  money  ? 


120  DENOMINATE   NUMBERS 

53.  1.  A  grocer  bought  100  melons  at  30  cents  a 
dozen.     How  much  did  they  cost  him? 

2.  How  many  years  old  is  a  man  whose  age  is  3 
score  and  10  ? 

3.  How  much  will  a  ream  of  paper  cost  at  10  cents 
a  quire? 

4.  A  ship  sank  where  the  depth  of  the  water  was 
20  fathoms.     How  many  feet  deep  was  it? 

5.  The  height  of  a  certain  horse  at  the  front  shoul- 
der was  15  hands.     What  was  its  height  in  feet? 

6.  A  gross  of  pens  was  bought  for  30  cents  and 
retailed  at  2  for  1  cent.     What  was  the  gain  ? 

7.  How  much  will  68  cucumbers  cost  at  24  cents  a 
dozen  ? 

8.  A  stationer  paid  $1.50  for  a  ream  of  paper  and 
sold  it  at  20  cents  a  quire.     How  much  did  he  gain  ? 

9.  If  I  buy  6  dozen  eggs  at  20  cents  a  dozen,  and 
sell  them  at  9  for  25  cents,  what  is  my  gain  ? 

10.  A  boy  rode  15  miles  on  a  bicycle  in  1  hour  and 
40  minutes.  How  long,  at  that  rate,  would  it  take  him 
to  make  a  journey  of  270  miles  ? 

11.  How  much  must  be  paid  for  a  ream  of  paper  at 
^  a  cent  a  sheet? 

12.  How  many  score  are  there  in  50?  in  75?  in  96? 

13.  A  stationer  pays  30  cents  per  gross  for  pens,  and 
retails  them  at  1  cent  apiece.  How  much  does  he  gain 
per  gross? 

14.  Eggs  bought  at  15  cents  per  dozen  are  sold  at  8 
for  25  cents.     What  is  the  gain  on  10  dozen  ?  , 


DENOMINATE   NUMBERS  121 

15.  How  much  must  be  paid  for  16  quires  of  paper 
at  $  2^  per  ream  ? 

16.  How  much  must  be  paid  for  one  gross  boxes 
of  crayon,  at  10  cents  a  box  ? 

17.  At  $2.70  per  gross  how  much  must  be  paid  for 
96  lead  pencils  ?  for  120? 

18.  Collar  buttons  bought  for  50  cents  per  gross 
were  sold  at  10  cents  per  dozen.  If  the  gain  was  $7, 
how  many  gross  were  sold  ? 

54.  1.  What  is  the  cost  of  3  bushels  3  pecks  of  oats, 
at  40  cents  per  bushel  ? 

2.  At  10  cents  a  quart,  what  is  the  cost  of  1  peck 
6  quarts  1  pint  of  cranberries  ? 

3.  How  much  will  a  piece  of  ribbon  2  yards  2  feet 
6  inches  long  cost,  at  12  cents  per  yard? 

4.  How  much  will  it  cost  to  build  a  fence  165  feet 
long,  at  $12  per  rod  ? 

5.  How  many  weeks  are  there  in  the  months  of 
September,  October,  and  November? 

6.  A  dealer  bought  60  gallons  of  wine  for  $50  and 
retailed  it  at  20  cents  a  pint.     How  much  did  he  gain  ? 

7.  Potatoes  bought  at  60  cents  per  bushel  are  re- 
tailed at  25  cents  per  peck.  How  many  bushels  must 
be  sold  to  gain  130? 

8.  How  many  days  were  there  in  the  year  1896, 
from  January  15  to  March  20? 

9.  A  lot  is  75  feet  square.  How  much  will  it  cost 
to  put  a  fence  around  it,  at  75  cents  a  yard  ? 


122  DENOMINATE   NUMBERS 

10.  If  1  bushel  3  pecks  of  chestnuts  cost  $5.60, 
what  is  the  price  per  bushel? 

11.  If  a  train  runs  §  of  a  mile  in  48  seconds,  what  is 
its  rate  per  hour? 

12.  If  2  pounds  5  ounces  of  butter  cost  74  cents, 
what  is  the  price  per  pound? 

13.  What  is  the  value  of  a  gold  watch  case  weighing 
50  pennyweights,  if  the  gold  is  worth  $  24  per  ounce  ? 

14.  The  circumference  of  a  wheel  is  very  nearly  3^ 
times  its  diameter.  How  many  feet  will  a  bicycle  hav- 
ing 28-inch  wheels  go  while  they  make  10  revolutions  ? 

15.  If  1  bushel  of  blackberries  that  cost  $  2  is  sold  at 
8  cents  per  quart,  how  much  is  gained  ? 

16.  How  many  bottles,  each  holding  one  gill,  can  be 
filled  with  one  gallon  of  turpentine  ? 

17.  A  merchant  buys  2\  dozen  handsaws  at  $18  per 
dozen.  If  he  sells  them  so  as  to  gain  50  cents  apiece, 
how  much  does  he  get  for  them  all  ? 

18.  What  will  be  the  cost  of  1  bushel  3  pecks  4 
quarts  of  potatoes  at  64  cents  per  bushel? 

19.  What  must  be  paid  a  gross  for  hairpins  so  that 
they  may  be  sold  at  10  cents  per  dozen,  and  40  cents  a 
gross  be  gained? 

20.  A  farmer  bought  3  tons  9  hundredweight  of 
plaster.  After  he  had  used  1  ton  8  hundredweight,  what 
was  the  value  of  the  remainder  at  $20  per  ton? 

21.  A  bedroom  6  yards  long  requires  27  square  yards 
of  carpet  to  cover  the  floor.     How  wide  is  the  room  ? 

22.  How  much  must  be  paid  for  3  pecks  5  quarts  of 
clover  seed  at  $6.40  per  bushel? 


DENOMINATE   NUMBERS  123 

23.  A  train  runs  from  New  York  to  Philadelphia,  a 
distance  of  90  miles,  in  2  hours  15  minutes.  What  is 
its  rate  per  hour  ? 

24.  How  many  square  feet  are  there  in  a  rectangle 
2  yards  long  and  30  inches  wide  ? 

25.  In  a  rod  there  are  5^  yards,  and  in  a  mile  320 
rods.     How  many  yards  are  there  in  a  mile  ? 

26.  How  many  months  and  days  are  there  in  f  of  a 
year?  in  |  of  a  year? 

27.  What  part  of  a  year  is  3  months  24  days?  1  month 
10  days  ?  5  months  10  days  ? 

28.  At  7  o'clock  my  clock  strikes  11 ;  how  many 
strokes  will  it  strike  at  11  o'clock? 

29.  If  a  man  can  earn  $66  in  1  month  20  days,  how 
much  does  he  earn  per  day,  counting  24  working  days 
per  month  ? 

30.  If  an  electric  car  goes  880  feet  per  minute,  how 
many  miles  does  it  go  per  hour? 

31.  How  much  should  be  charged  for  a  gold  ring, 
weighing  4  pennyweights  12  grains,  at  $24  per  ounce  ? 

32.  How  many  square  yards  are  there  in  the  walls 
of  a  room  16|  feet  long,  121  feet  wide,  and  10  feet 
high? 

33.  How  much  must  be  paid  for  3  boards,  each  16 
inches  wride  and  20  feet  long,  at  5  cents  a  square  foot  ? 

34.  When  2  pounds  14  ounces  of  beef  cost  46  cents, 
how  much  must  be  paid  for  1  pound  12  ounces  ? 

35.  Having  8  tons  15  hundredweight  of  coal  in  my 
cellar,  I  burn  |-  of  it.  What  is  the  value  of  what  is  left, 
at  $41  per  ton? 


124  DENOMINATE   NUMBERS 

36.  If  a  man  can  walk  If  miles  in  20  minutes,  how 
long  will  it  take  him  to  walk  21  miles  ? 

37.  A  merchant  bought  20  pounds  of  tea  for  $10. 
He  sold  £  of  it  for  If  times  what  it  all  cost.  How 
much  did  he  get  for  it  per  pound? 

38.  How  long  a  piece  of  carpet  27  inches  wide,  will 
contain  exactly  2  square  yards  ? 

39.  A  field  40  rods  wide,  sold  at  $80  per  acre, 
brought  $2400.     How  long  was  the  field? 

40.  Find  the  number  of  cubic  feet  of  air  in  a  room 
20  feet  long,  15  feet  wide,  and  10  feet  high. 

41.  If  a  watch  gained  1  minute  15  seconds  per  day, 
how  much  did  it  gain  during  February  1897  ? 

42.  How  many  flagstones,  each  4  feet  long  and  2 
feet  wide,  will  be  needed  to  lay  a  crossing  120  feet  long 
and  6  feet  wide  ? 

43.  How  much  is  received  for  a  barrel  of  apples 
containing  2^  bushels,  if  they  are  sold  for  10  cents  per 
half  peck? 

44.  A  man  divided  9  gallons  2  quarts  1  pint  of  milk 
equally  among  seven  poor  families.  How  much  did 
each  receive  ? 

45.  How  many  visiting  cards,  each  2  inches  long 
and  1^  inches  wide,  can  be  cut  from  a  piece  of  card- 
board 2  feet  1  inch  long  and  1  foot  4  inches  wide  ? 

46.  Each  of  7  milk  cans  contains  8  gallons  2  quarts 
and  1  pint  of  milk.  How  much  milk  is  there  in  them 
all? 

47.  How  many  3-inch  cubes  can  be  cut  from  a  block 
of  wood  1  foot  long,  6  inches  wide,  and  6  inches  thick  ? 


PERCENTAGE 


55.     1.    What  part  of  anything  is  20%  of  it? 

Note:  —  The  expression  Per  Cent  means  by  the  hundred.     The 
sign  of  Per  Cent  is  %. 

Solution  :  —  20  %  of  anything  is  ffa  or  J,  of  it. 

2.  What   part   of    anything   is   5%    of   it?      25%? 
50%?     80%?     75%?     100%? 

3.  What   part   of   anything   is  15%   of   it?     35%? 
45%?    55%?    75%?     95%? 

4.  What  part  of  anything  is  12i%  of  it?     16|%? 
331%?     37i%?     62iy,?     87J%  ? 

Solution:  — 12*  %  =  l?i  =  J?5.  =  -• 
*/0      100     200     8 

5.  What  is  30%  of  60  ?     25%  of  200  ?     50%  of  90  ? 
3%  of  300?    40%  of  400? 

Solution  :  —  30%  of  anything  is  T%  of  it ;  therefore  30  %  of  60  is 
A  of  60,  or  18. 

6.  What  is  12|%  of  96?     331%  0f  900?     371%  of 
$48?     871%  of  1800?     66|%  of  300? 

7.  A  gain  of  25%   was  made  on  an  investment  of 
$480.     How  much  was  gained  ? 

8.  I  paid  $180  for  a  horse,  and  sold  it  at  a  gain  of 
%.     How  much  was  gained  ? 

125 


126  PERCENTAGE 

9.    How  much,  is  f  %  of  $4800  ? 

Solution  :  — 1%  or  Tfa  of  $4800  is  $48,  hence  }%  of  $4800  is 
f  of  $48,  or  $36. 

Therefore  f  %  of  $4800  is  $36. 

10.  How  much  is  f%  of  $6600  ?  \%  of  $800  ?  f  % 
of  $8800?     £%  of  600  bushels? 

11.  How  much  is  \\%  of  $3600  ?  If  %  of  900  tons? 
%\%  of  $900?     3£%  of  3000  pounds? 

12.  Of  $250  deposited  in  a  bank,  8%  was  withdrawn. 
How  much  was  withdrawn  ? 

13.  A  farmer  raised  375  bushels  of  potatoes,  and 
reserved  8%  of  them  for  his  own  use.  How  many 
bushels  were  reserved? 

14.  Wood  bought  at  $5  a  cord  was  sold  at  a  gain  of 
40%.     How  much  was  gained  on  each  cord? 

15.  A  man  lost  by  a  sale  37^%  of  the  value  of  a 
horse  that  cost  him  $240.     How  much  did  he  lose? 

16.  If  62|%  of  $400  is  \  of  the  cost  of  a  coach, 
how  much  does  it  cost  ? 

17.  A  man  who  earns  $250  a  month,  regularly  puts 
25%  of  it  in  a  savings  bank.  How  much  does  he  put 
in  the  bank  in  a  year  ? 

18.  I  bought  6  horses  at  $180  each,  and  sold  them  at 
a  gain  of  33^%.     How  much  was  gained  on  all? 

19.  Which  is  the  better  and  how  much,  to  sell  $  400 
worth  of  goods  at  30%  profit,  or  $3000  worth  at  5% 
profit  ? 

20.  Having  $300,  I  paid  30%  for  board,  20%  for 
clothing,  and  15%  for  other  expenses.  How  many 
dollars  were  there  remaining  ? 


PERCENTAGE  127 

56.     1.    What  per  cent  of  anything  is  f  of  it  ? 
Solution  :  —  The  whole  of  anything  is  |$#  or  100  %  of  it ;  hence 
f  of  it  is  f  of  100%  of  it,  or  37J%. 

2.  What  per  cent  of  a  number  is  -J  of  it  ?     -£$  ?     \  ? 

i?  j?  t?  |?  |? 

3.  What  per  cent  of  my  income  is  -^  of  it  ?  ^  ?    \  ? 

I?  i?  i?  t?  i? 

4.  If  a  boy  lost  |  of  his  marbles,  what  per  cent  did 
he  lose  ?     What  per  cent  had  he  left  ? 

5.  A  man  expended  l  of  his  money  for  a  hat,  and 
the  remainder  for  an  overcoat.  What  per  cent  of  his 
money  did  each  cost  ? 

6.  After  ^  of  a  crop  of  potatoes  had  been  spoiled, 
|  of  the  remainder  was  sold,  and  the  rest  reserved  for 
seed.  What  per  cent  was  sold,  and  what  per  cent  was 
reserved  for  seed  ? 

7.  What  part  of  $  8  is  $  5  ?  How  many  hundredths 
of  $8  is  $5  ?     What  per  cent  of  $8  is  $  5  ? 

Solution:  — Since  1 5  is  f  of  9 8,  $5  is  ||£  or  62£%  of  $8. 
Therefore,  etc.  10° 

8.  What  part  of  12  is  3  ?  What  per  cent  of  12  is 
3  ?  of  15  is  5  ?  of  20  is  4  ?  of  24  is  18  ? 

9.  What  part  of  25  is  15  ?  What  per  cent  of  25  is 
15?  of  35  is  25  ?  of  45  is  35?  of  75  is  65  ? 

10.  What  per  cent  of  2  is  4  ?  of  6  is  9  ?  of  10  is  14  ? 
of  8  is  20  ?  of  9  is  12  ? 

11.  What  per  cent  of  f  is  J  ?  of  f  is  f  ?  of  f  is  f  ? 
of  f  is  |?  of  f  is  J? 

Suggestion  :  —  Reduce  the  fractions  to  fractions  having  a  com- 
mon denominator. 


128  PERCENTAGE 

12.  What  per  cent  of  21  is  l\  ?  of  3£  is  2£  ?  of  2} 
is  If?  of  4is2£?  of  3£isl|? 

13.  A  coat  that  cost  $25  was  sold  for  $45.  What 
was  the  gain  per  cent  ? 

Note  :  —  The  gain  or  loss  is  always  computed  as  a  certain  part 
or  per  cent  of  the  cost. 

14.  A  drover  bought  six  horses  for  $900,  and  sold 
them  at  $  225  each.     Find  the  gain  per  cent. 

15.  A  boat  was  rowed  150  miles  down  a  river,  and 
was  carried  by  the  current  50  miles  farther.  What  per 
cent  of  the  entire  distance  was  due  to  the  current,  and 
what  per  cent  to  the  rowing  ? 

16.  I  sold  a  wagon  for  $  200,  thereby  gaining  $  50. 
What  was  the  cost  ?     What  was  the  gain  per  cent  ? 

17.  An  apple  dealer  bought  a  lot  of  apples  at  4  for  3 
cents  and  sold'  them  at  4  for  5  cents.  What  was  his 
gain  per  cent? 

18.  A  watch  was  sold  for  $  150,  which  was  \\  times 
its  cost.     Find  the  gain  per  cent  and  the  cost. 

19.  A  dozen  overcoats  were  sold  for  $  400.  If  they 
cost  $25  each,  what  per  cent  was  gained? 

20.  A  hardware  dealer  gets  for  2  bicycles  exactly 
what  3  cost  him.     What  is  his  gain  per  cent? 

21.  Eggs  bought  at  15  cents  a  dozen  are  sold  at  10 
for  25  cents.     What  per  cent  is  gained? 

22.  A  merchant  bought  150  barrels  of  flour.  He  sold 
20%  of  it  at  cost  and  on  the  remainder  he  gained  40%. 
What  per  cent  did  he  gain  on  the  whole  ? 


PERCENTAGE  129 

57.  1.  By  selling  a  horse  for  $  40  more  than  it  cost, 
a  man  gained  20%.     How  much  did  the  horse  cost? 

Solution: — $40  was  20%,  or  £,  the  cost  of  the  horse ;  hence  the 
cost  of  the  horse  was  5  times  $40,  or  $200.     Therefore,  etc. 

2.  On  hay  sold  at  $  11  per  ton  there  was  a  profit  of 
37|%.     How  much  did  it  cost? 

Suggestion  :  —  Since  the  hay  was  sold  at  a  profit  of  37|  %,  or  f  of 
the  cost,  the  selling  price  was  -y~  of  the  cost. 

3.  A  man  sold  his  watch  for  $60,  and  by  so  doing 
lost  25%.     How  much  did  it  cost  him  ? 

Suggestion  :  —  Since  he  lost  25%,  or  J,  of  the  cost,  he  sold  it  for 
f  of  the  cost. 

4.  A  farmer  sold  62^%  of  his  land,  and  had  120 
acres  left.     How  many  acres  did  he  own  at  first? 

5.  If  60%  of  the  coal  in  my  cellar  is  18f  tons,  how 
many  tons  are  there? 

6.  .  A  student  sold  his  books  for  $  90,  which  was  at 
a  loss  of  25%.     How  much  did  they  cost  him? 

7.  A  sold  a  horse  to  B  at  a  gain  of  20%,  and  B  sold 
it  to  C  for  #198,  which  was  at  a  gain  of  10%.  How 
much  did  A  pay  for  the  horse? 

8.  A  horse  and  carriage  were  sold  for  85%  of  their 
cost,  by  which  there  was  a  loss  of  $  75.  How  much  did 
they  cost? 

9.  By  reducing  ribbon  from  40  cents  to  35  cents  a 
yard,  a  merchant  diminished  his  gain  by  20%.  How 
much  did  it  cost  him  per  yard? 

10.  A  coal  merchant  raised  the  price  of  coal  60  cents 
per  ton,  and  by  so  doing  he  gained  50%  instead  of  33 £%. 
How  much  did  the  coal  cost  him  per  ton? 

MILNE    MENTAL  —  ft 


130  PERCENTAGE 

11.  After  15%  of  a  regiment  of  soldiers  has  been 
killed  there  are  680  left.  How  many  men  were  in  the 
regiment  at  first? 

12.  By  selling  cloth  at  $  2  J  per  yard  a  merchant  lost 
16|%.     For  how  much  must  he  sell  it  to  gain  16|%? 

13.  If  my  expenses  were  increased  12£%,  my  monthly 
savings  would  be  $21  less  than  they  are.  How  much 
do  I  get  a  month,  if  I  save  75%  as  much  as  I  spend? 

14.  A  man  paid  $60  for  a  watch,  which  was  20% 
less  than  its  value,  and  he  sold  it  for  20%  more  than 
its  value.     What  per  cent  did  he  gain? 

15.  A  jeweler  sold  2  watches  at  $  60  each  ;  on  one  he 
lost  20%,  and  on  the  other  he  gained  20%.  Did  he 
gain  or  lose  by  the  transaction,  and  how  much? 

16.  By  selling  a  piano  for  40%  less  than  the  cata- 
logue price,  a  dealer  made  a  profit  of  25%.  How  much 
did  it  cost  him,  if  the  catalogue  price  was  $500? 

17.  A  drover  sold  two  horses  at  $120  apiece.  On 
one  he  gained  20%,  and  on  the  other  he  lost  33|%. 
How  much  did  he  gain  or  lose  by  the  transaction? 

18.  Some  furniture  was  bought  for  16|%  less  than 
its  value,  and  sold  for  16|%  more  than  its  value. 
What  was  its  value,  if  the  difference  between  the  cost 
and  the  selling  price  was  $  60  ? 

19.  A  dealer  sold  120  barrels  of  flour  for  $  792,  which 
was  12%  less  than  he  paid  for  it.  How  much  did  it 
cost  per  barrel  ? 

20.  Two  persons  commenced  business  with  equal 
capital.  One  gained  25%,  the  other  37%.  What  was 
their  capital  if  the  difference  between  their  gains  was 
$1080? 


PERCENTAGE  131 

58.  1.  An  agent  sells  goods  for  $800,  and  gets  5% 
commission  for  selling  them.  How  much  does  he 
receive  for  his  services? 

Solution  :  —  At  a  commission  of  5  %  the  agent  receives  T^,  or  2^, 
of  the  amount  of  the  sale,     ^o  of  •  800  is  •  *0.     Therefore,  etc. 

2.  A  collector  gets  8%  commission  and  collects 
$5000.     How  much  does  he  get  for  his  services? 

3.  Mr.  Brown  paid  12|%  for  the  collection  of  a  note 
for  $8000.     How  much  did  he  pay? 

4.  An  agent  sold  a  house  for  $9500,  receiving  2% 
commission  for  selling  it.  How  much  did  he  receive 
for  his  services? 

5.  A  commission  of  |%  was  allowed  an  agent  for 
selling  $6000  worth  of  cotton.  How  much  did  the 
agent  receive,  and  how  much  the  owner  of  the  cotton? 

6.  A  lawyer  secured  a  judgment  of  $  7500  against  a 
railroad  company,  for  damages  to  a  client.  The  lawyer 
was  to  receive  20%  for  his  services.  How  much  was 
left  for  the  client  ? 

7.  A  broker  sold  for  a  customer  railroad  stock 
whose  face  or  par  value  was  $  20,000,  at  a  commission 
of  \%.     Find  his  commission. 

Note:  —  Commission  of  a  broker,  or  brokerage,  is  computed 
upon  the  face  or  par  value  of  the  securities  bought  or  sold. 

8.  A  Western  bank  charged  \%  for  collecting  a 
draft  on  New  York  for  $1200.  How  much  was  the 
charge? 

9.  An  auctioneer  sold  goods  to  the  amount  of  $  2400 
at  a  commission  of  2£%.     What  was  his  commission? 


132  PERCENTAGE 

10.  A  traveling  salesman  received  a  commission  of 
10%  on  his  sales.  His  average  monthly  sales  during 
1896  amounted  to  $1250.  Find  his  commission  for  the 
year. 

11.  A  miller  takes  10%  toll  for  grinding  wheat. 
How  much  does  his  mill  earn  in  6  days,  if  it  grinds  450 
bushels  per  day,  and  if  wheat  is  worth  $ 1  per  bushel  ? 

12.  An  agent's  commission  at  \\  %  for  selling  a  house 
amounted  to  $300.  How  much  was  received  for  the 
house  ? 

Solution  :  —  1  \  %  or  2g0,  of  the  value  of  the  house  is  therefore 
$300;  2$0  of  it  is  $100;  and  the  value  of  the  house  is  200  times 
$  100,  or  $20,000.     Therefore,  etc. 

13.  A  collector  whose  commission  was  5%  paid  in, 
after  deducting  his  commission,  $  38,000.  How  much 
was  his  commission  ? 

Suggestion: —  He  paid  in  only  95%  of  the  amount  collected. 

14.  A  broker  sold  bonds  on  which  his  commission 
at  |%  was  $375.  What  wras  the  par  value  of  the 
bonds  ? 

15.  An  agent  sold  cotton  on  a  commission  of  6|%. 
If  the  owner  received  $4500,  what  was  the  agent's  com- 
mission ? 

16.  I  sent  my  agent  $8400,  with  which  to  purchase 
goods  after  deducting  his  commission  of  5%.  How 
much  was  expended  for  goods? 

Suggestion:  —  Since  the  agent  receives  for  his  services  5%,  or 
-}■$  of  the  sum  expended  for  goods,  and  since  $8400  includes  the 
sum  expended  for  goods  and  his  commission,  $8400  must  be  \\  of 
the  sum  expended  for  goods. 


PERCENTAGE  133 

17.  An  agent  received  $648  with  which  to  purchase 
hogs  at  $6  each,  after  his  commission  of  8%  for  pur- 
chasing was  deducted.     How  many  could  he  buy  ? 

18.  I  sent  a  broker  $6200  to  invest  in  the  stock  of  a 
sugar  refining  company,  after  deducting  his  commission 
of  3^%.     How  much  was  his  commission? 

19.  How  many  bushels  of  wheat  at  80  cents  a  bushel 
can  an  agent  purchase  with  $  8100,  after  deducting  his 
commission  of  \\°fo  ? 

20.  How  many  shares  of  stock  at  $  25  per  share  can  a 
broker  pay  for  with  15200,  if  he  deducts  a  commission 
or  brokerage  of  4%  ? 

59.  1.  How  much  must  be  paid  for  an  insurance 
policy  for  $2000  on  a  house,  if  the  premium  is  1J%  ? 

Solution  :  —  Since  a  premium  of  \\%  is  paid,  the  premium  is  1|%, 
or  jfo,  of  the  policy.     ?fa  of  $2000  is  $30.     Therefore,  etc. 

2.  How  much  will  it  cost  to  insure  a  ship  for  $  60,000, 
at  2%  premium? 

3.  A  farmer  insures  his  barn  for  $3500,  paying  a 
premium  of  2%.     How  much  does  the  insurance  cost? 

4.  A  man  owns  |  of  a  ship  that  is  worth  $100,000. 
He  insures  his  share  at  a  premium  of  1|  %.  How  much 
is  the  premium? 

5.  A  merchant  insures  his  goods  for  $5000,  paying 
a  premium  of  2|%.  How  much  does  the  insurance 
cost? 

6.  Find  the  cost  of  an  insurance  policy  for  $  4500  at 
1|%  premium. 

7.  A  house  worth  $18,000  is  insured  for  |  of  its 
value  at  1|%  premium.    What  is  the  cost  of  insuring  it? 


134  PERCENTAGE 

8.  A  ship  worth  $50,000  is  insured  for  |  of  its  value 
at  3%  premium.  If  the  ship  is  wrecked,  how  much  do 
the  owners  lose,  including  the  premium  ? 

9.  It  cost  $90  to  insure  my  house  for  f  of  its  value, 
at  a  premium  of  1£%.     What  was  its  value  ? 

Suggestion: — $90  was  §  of  the  sum  required  to  insure  the 
house  at  its  full  value  at  the  given  rate. 

10.  The  premium  at  -|  of  1%  for  insuring  some  goods 
is  $  20.     What  is  the  amount  of  the  policy  ? 

11.  A  house  worth  $12,000  is  insured  for  f  of  its 
value,  at  a  cost  of  $150.    What  is  the  rate  of  premium? 

12.  A  and  B  insure  goods  for  $3400  at  2%  premium. 
What  premium  should  each  pay  if  §  of  A's  share  of  the 
goods  equals  |  of  B's  share  ? 

13.  If  $120  was  paid  for  insuring  horses  worth  $80 
apiece  at  1|%  premium,  how  many  horses  were  there? 

60.   1.   What  is  the  interest  of  $300  for  1  year  at  6%? 

Solution:  —  The  interest  for  1  year  at  6%  is  T%$  of  the  princi- 
pal. T£s  of  $  300  is  $  18.  Therefore,  the  interest  of  $  300  for  1  year 
at  6%  is  $18. 

Note:  —  In  computing  interest,  a  year  is  generally  assumed  to 
be  12  months,  and  a  month  30  days. 

In  the  following  examples  those  divisions  of  the  year  and  month 
will  be  adopted. 

Find  the  interest  of  : 

2.  $400  for  1  year  at  4%.  6.  $500  for  1  year  at  7%. 

3.  $800  for  1  year  at  10%.  7.  $200  for  1  year  at  12%. 

4.  $600  for  1  year  at  8%.  8.  $100  for  1  year  at  11%. 

5.  $300  for  1  year  at  5%.  9.  $900  for  1  year  at  6%. 


PERCENTAGE  135 

10.  $150  for  1  year  at  4%. 

11.  $750  for  1  year  at  8%. 

12.  $800  for  2  years  at  b\%. 

13.  $150  for  4  years  at  41%. 

14.  $400  for  31  years  at  4%. 

15.  $250  for  2  years  at  6%. 

16.  $300  for  21  years  at  8%. 

17.  $750  for  4  years  at  5%. 

18.  $175  for  5  years  at  5%. 

19.  $350  for  3§  years  at  6%. 

To  what  part  of  the  principal  is  the  interest  equal: 

20.  In  2  years  5  months  at  6%  ? 

Solution  :  —  2  years  5  months  are  2T\  years,  or  f f  of  a  year. 
At  6  %  for  1  year,  the  interest  is  Tf -$  of  the  principal,  and  for  f  §  of  a 
year  f  §  of  jf^,  or  ffa  of  the  principal.     Therefore,  etc. 

21.  In  2  years  6  months  at  4%  ? 

22.  In  3  years  4  months  at  9%  ? 

23.  In  4  years  2  months  at  6%  ? 

24.  In  2  years  8  months  at  3J%  ? 

25.  In  3  years  3  months  at  5%  ? 

26.  In  8  years  7  months  at  4%  ? 

27.  In  1  year  10  months  at  3%  ? 

28.  In  2  years  5  months  18  days  at  5%  ? 

Solution  :  — 18  days  are  f  of  a  month.  Therefore  5  mo.  18  da. 
equal  5|  months  or  258  months.  Since  1  month  =  ^  year, 2/  months  = 
II  or  A  year-   Therefore  2  yr.  5  mo.  18  da.  =  2T77  years,  or  (j  years. 

At  5%  the  interest  for  1  year  equals  ^  of  the  principal,  and  for 
f |  years  f  J  of  ^,  or  gVo,  of  the  principal.     Therefore,  etc. 


136  PERCENTAGE 

To  what  part  of  the  principal  is  the  interest  equal : 

29.  In  3  yr.  6  mo.  15  da.  at  4%  ? 

30.  In  1  yr.  5  mo.  20  da.  at  9%  ? 

31.  In  2  yr.  4  mo.  12  da.  at  5%  ? 

32.  In  4  yr.  5  mo.  10  da.  at  3%  ? 

33.  In  5  yr.  3  mo.  24  da.  at  12%  ? 

34.  In  2  yr.  1  mo.  5  da.  at  8%  ? 

35.  In  3  yr.  3  mo.  3  da.  at  10%  ? 

36.  In  2  yr.  5  mo.  15  da.  at  6%  ? 

37.  What  is  the  interest  of  $1000  for  60  days  at 
6%  ? 

Solution:  —  At  6%  the  interest  for  1  year  equals  jfo  of  the 
principal.  Since  60  days  are  considered  £  of  a  year,  the  interest 
for  60  days  is  TJT  of  the  principal ;  yfo  of  $  1000  is  1 10.  There- 
fore, etc. 

What  is  the  interest  of  : 

38.  $8750  for  60  da.  at  6%  ? 

39.  $3600  for  30  da.  at  6%  ? 

40.  $5000  for  60  da.  at  3%  ? 

41.  $6000  for  90  da.  at  4%  ? 

42.  $4000  for  30  da.  at  9%  ? 

43.  $4800  for  30  da.  at  5%  ? 

44.  $6600  for  90  da.  at  8%  ? 

45.  $1200  for  60  da.  at  7%  ? 

46.  $3000  for  90  da.  at  6%  ? 

47.  $2450  for  30  da.  at  6%  ? 

48.  $36.80  for  90  da.  at  9%  ? 


PERCENTAGE  137 

61.  1.  What  is  the  amount  of  $2400  for  2  yr.  6 
mo.  at  6%  ? 

Solution: —  At  6%,  the  interest  of  any  sum  for  2  yr.  6  mo.  is 
y1^,  or  2%,  of  the  principal,  and  the  amount  for  the  same  time  is  §§ 
of  the  principal.     f$  of  82400  is  $2760.    Therefore,  etc. 

What  is  the  amount  of  : 

2.  $3600  for  5  yr.  at5%? 

3.  $120  for  6  yr.  3  mo.  at  4%  ? 

4.  $300  for  5  yr.  6  mo.  at  6%  ? 

5.  $4000  for  3  yr.  3  mo.  at  8%  ? 

6.  $640  for  2  yr.  6  mo.  at  5%  ? 

7.  $800  for  1  yr.  5  mo.  at  12%  ? 

8.  $1000  for  3  yr.  8  mo.  at  3%  ? 

9.  $6000  for  3  yr.  3  mo.  15  da.  at  8%  ? 

10.  $400  for  1  yr.  1  mo.  24  da.  at  5%  ? 

11.  $240  for  60  da.  at  6%? 

12.  $900  for  90  da.  at  8%? 

13.  $6000  for  30  da.  at  4%  ? 

14.  $4800  for  45  da.  at4%? 

15.  $9600  for  75  da.  at  5%? 

16.  $3000  for  5  yr.  4  mo.  18  da.  at  4%  ? 

17.  $  1200  for  3  yr.  3  mo.  10  da.  at  6%  ? 

18.  $1500  for  2  yr.  6  mo.  20  da.  at  3%  ? 

19.  Divide  the  amount  of  $1000  for  3  yr.  at  5%, 
between  A  and  B,  so  that  A's  share  shall  be  §  of  B's. 

20.  A  and  B  wish  to  divide  the  amount  of  $5000  for 
4  years,  at  5%,  into  two  parts,  so  that  A  may  have 
twice  as  much  as  B.     Find  their  shares. 


138  PERCENTAGE 

21.  The  amount  of  my  money  for  2  years  and  6 
months  at  6%  is  1 250  less  than  the  amount  for  4  years 
at  5%.     How  much  have  I? 

Suggestion  :  —  The  amount  of  my  money  in  2  yr.  6  mo.  at  6% 
will  be  |f  of  the  principal,  and  for  4  yr.  at  5%  \  j  of  the  principal. 

22.  My  brother  and  I  had  together  $3000  at  interest 
for  4  years  6  months  at  4%.  If  the  interest  was  divided 
so  that  his  share  was  twice  mine,  how  much  did  each 
receive  ? 

23.  I  gave  a  note  for  18000,  which  I  paid  3  years  6 
months  afterwards,  with  interest  at  4£%.  What  was 
the  amount  due  ? 

62.  1.  What  principal  will  yield  $96  interest  in  2 
years  8  months  at  6%  ? 

Solution  :  —  The  interest  of  any  sum  for  2  yr.  8  mo.  at  6  %  is 
t1^  of  the  principal.  Hence  $96  is  &%  of  the  principal ;  Tfo  of  the 
principal  is  TV  of  $96,  which  is  $6,  and  the  principal  is  100  times 
$  6,  or  $  600.     Therefore,  etc. 

2.  What  principal  will  in  3  years  9  months  at  4% 
yield  $150  interest? 

3.  Find  the  principal  that  will  yield  $680  interest 
in  8  months  15  days  at  6%. 

4.  What  principal  will  yield  $45.75  interest  in  60 
days  at  6%? 

5.  What  principal  will  yield  $  65  interest  in  30  days 
at6%? 

6.  What  principal  at  4%  yields  $150  interest  in  90 
days? 

7.  What  principal  will  yield  $13.20  interest  in  2 
years  9  months  at  4%  ? 


PERCENTAGE  139 

8.  How  much  do  I  owe,  if  in  3  years  3  months  15 
days,  the  interest  on  the  debt  at  8%  is  $158? 

9.  A  and  B  put  at  interest  equal  sums  of  money. 
A's  money,  in  3  years  5  months  at  6%,  yields  $81  less 
interest  than  B's  in  4  years  3  months  at  8%.  How 
much  had  each  on  interest? 

10.  The  interest  of  a  sum  for  6  years  at  5%  is  $600 
more  than  its  interest  for  3  years  at  6%.    Find  the  sum. 

11.  Two  sons  inherited  equal  sums  of  money.  One 
put  |  of  his  money  at  interest,  the  other  |  of  his,  each 
at  6%.  In  2  years  8  months  their  combined  interest 
was  $  2720.     How  much  did  each  inherit  ? 

Suggestion  :  —  If  each  had  put  all  his  money  at  interest  at 
the  given  rate,  the  interest  of  each  would  have  been  y1^  of  the  sum 
inherited.  But  since  one  invested  only  §  of  his  money,  his  interest 
was  only  §  of  y1^,  or  y1/^,  of  the  inheritance,  and  since  the  second 
invested  only  f  of  his,  his  interest  was  only  §  of  Ty7,  or  T\^,  of  his 
inheritance. 

12.  The  money  paid  for  a  horse  and  wagon  will,  in  1 
year  8  months  at  6%,  yield  $32  interest.  How  much 
was  paid  for  each  if  f  of  the  cost  of  the  wagon  was  f 
the  cost  of  the  horse  ? 

13.  A  merchant  who  cleared  12%  annually  on  his 
investment  was  forced  by  poor  health  to  give  up  his 
business  and  to  lend  his  money  at  7%.  His  income 
was  thus  reduced  $6800  in  2  years  3  months  and  6 
days.     What  was  his  investment? 

14.  On  April  15,  1897,  a  man  bought  400  sheep  and 
gave  in  payment  his  note  on  interest  at  6%.  When  he 
paid  the  note  on  June  30,  1897,  the  interest  was  $25. 
How  much  did  the  sheep  cost  per  head  ? 


140  PERCENTAGE 

63.  1.  What  principal  will  in  2  years  10  months  at 
6%  amount  to  $585? 

Solution:  —  The  interest  of  any  sum  for  2  yr.  10  mo.  at  6%  is 
$fo  of  the  principal,  and  the  amount  for  that  time  equals  }£$  of  the 
principal.  Hence,  $585  is  j£J  of  the  principal ;  TJ^  of  the  principal 
is  T\7  of  $  585,  which  is  $  5 ;  and  the  principal  is  100  times  $  5,  or 
$500.     Therefore,  etc. 

2.  What  principal  will  amount  to  $342  in  3  years 
6  months  at  4%  ? 

3.  What  sum  will  in  90  days  at  4%  amount  to  $8888? 

4.  What  sum  will  in  60  days  at  6  %  amount  to  $  2020  ? 

5.  A  man  borrowed  a  sum  of  money  at  6%,  for 
3  years  8  months  20  days.  At  the  end  of  the  time  he 
owed  $  3670.     How  much  did  he  borrow  ? 

6.  A  loaned  some  money  to  a  friend  for  6  months 
20  days  at  10%.  At  the  end  of  the  time  the  entire 
debt  was  $3800.     How  much  was  loaned? 

7.  A's  money  is  twice  B's,  and  the  amount  of  their 
money  for  3  years  5  months  10  days  at  6%  is  $3620. 
How  much  has  each  ? 

8.  If  |  of  M's  money  is  equal  to  |  of  N's,  and  the 
amount  of  their  money  at  interest  for  1  year  8  months 
at  6%  will  be  $18,700,  how  much  has  each? 

9.  A's  money  is  f  of  B's,  and  J  of  their  money  at 
interest  for  2  years  3  months  at  4%  amounts  to  $1199. 
How  much  has  each  ? 

10.  If  the  amount  of  $10,000  for  3  years  9  months 
at  8%  is  divided  into  two  parts  that  are  to  each  other 
as  8  to  5,  it  will  give  respectively  ^  of  A's  money  and 
|  of  B's.     How  much  has  each  ? 


PERCENTAGE  141 

64.  1.  In  what  time  will  $300  at  5%  yield  880 
interest  ? 

Solution:  —  In  one  year,  at  5%,  the  interest  on  $300  is  $15. 
To  yield  $  80  interest,  will  require  as  many  years  as  $  1 5  is  con- 
tained times  in  $  80,  or  5£  years.  The  time  is,  therefore,  5  years 
4  months. 

2.  In  what  time  will  $  500  at  6  %  yield  $120  interest  ? 

3.  In  what  time  at  6  %  will  $  8000  yield  $  80  interest  ? 

4.  In  what  time  at  4  %  will  $  6500  yield  $  65  interest  ? 

5.  A  note  for  $3000  at  5%  was  not  paid  until  the 
interest  was  $400.     How  long  did  it  run? 

6.  A  pawnbroker  loaned  $50  on  a  watch,  charging 
12%  interest.  The  watch  was  redeemed  when  the  in- 
terest was  $  11.     How  long  was  it  in  pawn  ? 

7.  In  what  time  at  8%  will  $90  yield  $36  interest? 

8.  In  what  time  will  $  180  at  5%  yield  $  30  interest  ? 

9.  The  amount  of  $800  for  a  certain  time  at  7%  is 
$1080.     Find  the  time. 

10.  A  certain  principal  doubled  itself  at  6%.  How 
long  was  it  at  interest? 

Suggestion  :  —  The  annual  interest  is  Tf  7  of  the  principal  and 
the  entire  interest  j§§  of  the  principal. 

11.  In  what  time  will  a  principal  double  itself  at 
5%  ?  at  8%  ?  at  4%  ?  at  20%  ?  at  25%  ? 

12.  In  what  time  will  a  principal  treble  itself  at 
10%  ?  at  12%  ?  at  5%  ?  at  40%  ?  at  50%  ? 

13.  A  debt  to  be  paid  after  a  certain  time  will 
amount  with  interest  at  5%  to  $  750,  and  with  interest 
at  8%  to  $840.     Find  the  debt  and  the  time. 

Suggestion  :  —  The  interest  of  the  debt  for  the  whole  time  at 
3%  =  $840 -$750. 


142  PERCENTAGE 

65.  1.  At  what  rate  per  cent  will  $60  in  3  years  6 
months  yield  $12.60  interest? 

Solution  :  —  At  1%,  the  interest  of  $  60  in  3  years  6  months  is 
12.10 ;  and  to  yield  $  12.60  interest,  the  rate  must  be  as  many  times 
1%  as  |2.10  is  contained  times  in  $12.60,  or  6  times.  The  rate  is, 
therefore,  6%. 

2.  At  what  rate  will   $90   in  5   years  yield  $18 
interest  ? 

3.  What  is  the  rate,  if  the  principal  is  $200,  the 
time  6  years,  and  the  interest  $90? 

4.  At  what  rate  will  $  300  in  2  years  8  months  yield 
$72  interest? 

5.  At  what  rate  will  $5000  in  90  days  yield  $50 
interest  ? 

6.  The  time  being  60  days,  the  principal  $8100, 
and  the  interest  $  81,  what  is  the  rate  ? 

7.  At  what  rate  per  cent  will  $600  in  5  years  yield 
$135  interest? 

8.  At  what  rate  per  cent  will  $750  in  2  years  7 
months  6  days  yield  $195  interest? 

9.  At  what  rate  per  cent  will  $1600  in  2  years  3 
months  15  days  yield  $440  interest? 

10.  At  what  rate  per  cent  will  $1200  in  4J  years 
amount  to  $1416? 

11.  When  the  principal  is  $775,  the  amount  $930, 
and  the  time  3  years  4  months,  what  is  the  rate  ? 

12.  The  amount  of  a  certain  principal  for  5  years  at 
a  certain  rate  is  $665^  and  for  8  years  at  the  same  rate 
it  is  $779.     What  are  the  rate  and  the  principal? 


PERCENTAGE  143 

66.  1.  A  man  gets  $75  per  month,  and  saves  20%  of 
it.     How  much  does  he  save  in  a  year? 

2.  I  bought  80  bushels  of  potatoes  at  50  cents  a 
bushel;  25%  of  them  were  unsalable,  but  the  rest  were 
sold  so  that  12^-%  was  gained  by  the  transaction.  How 
much  did  they  sell  for  per  bushel  ? 

3.  Two  coats  were  sold  at  $30  each.  On  one  20% 
was  gained;  on  the  other  20%  was  lost.  How  much 
was  the  gain  or  loss  ? 

4.  By  selling  a  horse  for  $180,  I  gain  20%.  For 
what  price  should  I  sell  it  to  gain  33^%? 

5.  What  per  cent  discount  does  a  piano  dealer  allow 
who  gives  a  discount  of  25%,  and  a  further  discount  of 
20%  from  the  remainder? 

6.  How  much  was  paid  for  a  piano  catalogued  at 
$600,  if  a  discount  of  30%  was  deducted,  and  another 
discount  of  20%  from  what  remained? 

7.  A  merchant  sold  cloth  at  $  2.40  per  yard,  thereby 
gaining  20%.  Later  he  marked  it  down  so  that  he  lost 
25%.     What  was  the  second  selling  price? 

8.  A  man  paid  20%  of  his  money  for  a  house,  and 
30%  of  the  remainder  for  a  store.  How  much  did  each 
cost  if  he  paid  $200  more  for  the  store  than  for  the 
house  ? 

9.  At  what  rate  per  cent  will  a  principal  double 
itself  in  16  years  8  months? 

10.  The  amount  of  a  certain  principal  at  a  certain 
rate  for  3  years  is  $552,  and  for  7  years,  $648.  Find 
the  principal  and  the  rate. 


144  PERCENTAGE 

11.  My  grocer  gets  20%  of  my  annual  salary,  and 
my  butcher  10%  of  the  remainder.  What  is  my  salary, 
if  my  grocer  gets  $  600  more  than  my  butcher  ? 

12.  A  farmer  raised  wheat  and  rye  in  quantities 
such  that  40%  of  his  wheat  was  equal  to  75%  of  his 
rye,  and  of  both  he  had  4600  bushels.  How  many 
bushels  of  each  did  he  raise  ? 

13.  How  much  money  has  A,  if  40%  of  his  money 
is  in  coin,  30%  of  it  is  in  bills,  and  the  remainder,  which 
is  1900,  is  loaned? 

14.  A  sold  a  horse  to  B  at  a  loss  of  20%  ;  B  sold  it 
to  C  for  $150,  and  by  so  doing  lost  25%.  How  much 
did  A  pay  for  the  horse  ? 

15.  Mr.  Brown  sold  his  horse  so  that  75%  of  what 
he  paid  for  it  was  equal  to  60%  of  the  selling  price. 
Did  he  gain  or  lose,  and  what  per  cent  ? 

16.  A  dealer  wishes  to  mark  the  price  of  a  piano  so 
that  after  allowing  to  the  buyer  a  discount  of  20%,  and 
also  20%  of  the  remainder,  he  may  get  $320  for  it. 
Find  the  marked  price. 

17.  How  must  a  coat  that  cost  $  30  be  marked  so 
that  there  may  be  a  profit  of  20%  after  a  discount  of 
10%  from  the  marked  price  has  been  allowed? 

18.  If  a  dealer  in  tea  always  gets  for  3  pounds  of 
tea  as  much  as  4  pounds  cost,  what  per  cent  does  he 
gain? 

19.  How  many  sheep  at  $5  each  must  I  buy,  so  that 
if  I  sell  them  at  a  gain  of  20%  I  may  make  a  profit  of 

$25? 


PERCENTAGE  145 

20.  By  selling  a  bale  of  goods  for  $  80  less  than  cost, 
there  was  a  loss  of  10%.  For  how  much  should  it  have 
been  sold  to  gain  25  %  ? 

21.  A  mixture  of  equal  parts  of  two  kinds  of  coffee, 
costing  18  and  22  cents  per  pound,  was  sold  so  as  to 
gain  25  %  •     What  was  the  selling  price  per  pound  ? 

22.  A  drover  has  horses,  oxen,  and  sheep,  in  all  1840. 
How  many  of  each  kind  has  he  if  the  number  of  oxen 
is  60%  of  the  number  of  sheep,  and  the  number  of 
horses  40  %  of  the  number  of  oxen  ? 

23.  There  is  a  number  such  that  30%  of  £  the  num- 
ber is  27  less  than  40%  of  f  of  it.     Find  the  number. 

24.  In  a  mixture  of  two  kinds  of  tea,  60%  of  it  cost 
40  cents  a  pound,  and  the  remainder  50  cents  a  pound. 
For  what  price  per  pound  should  it  be  sold  to  gain  25%  ? 

25.  A  boy  had  some  marbles  of  which  he  lost  20%. 
He  then  purchased  a  number  equal  to  50%  of  what  he 
had  left,  after  which  he  had  72.  How  many  had  he  at 
first? 

26.  If  a  ton  of  hay  is  bought  for  80%  of  the  market 
price  and  sold  at  a  gain  of  37^%,  at  what  per  cent  above 
the  market  price  is  it  sold  ? 

27.  A  and  B  engage  in  trade,  A  furnishing  60%  of 
the  capital,  and  B  the  rest.  At  the  end  of  the  year, 
after  a  gain  of  25%,  the  capital  and  gain  amount  to 
$2000.     What  is  each  man's  share  of  the  gain? 

28.  After  expending  $40  more  than  40%  of  his 
money,  a  clerk  has  $140  left.  How  much  had  he  at 
first? 

MILNE    MENTAL  —  10 


146  PERCENTAGE 

29.  I  marked  cloth  to  sell  at  a  gain  of  40%,  but  on 
account  of  using  an  incorrect  yard  measure  I  gained 
only  30%.     What  was  the  length  of  the  measure? 

30.  I  pay  $48  for  insuring  my  house  worth  $8000  at 
|%.     For  what  part  of  its  value  is  my  house  insured  ? 

31.  How  much  money  should  I  send  my  agent  that 
he  may  buy  2000  pounds  of  tea  at  35  cents  a  pound  and 
retain  his  commission  of  4%  of  the  sum  invested? 

32.  A  dealer  in  machinery  asked  for  a  reaper  30% 
more  than  it  cost.  He  finally  took  10%  less  than  his 
asking  price,  and  gained  $  34.     How  much  did  he  ask  ? 

33.  An  article  exposed  to  damp  air  absorbed  6  ounces 
of  water.  It  then  weighed  5  pounds.  What  per  cent 
of  this  weight  was  the  water  absorbed  ? 

34.  What  per  cent  above  cost  must  a  man  mark  his 
goods  in  order  that  he  may  take  off  10%  from  the 
marked  price  and  still  make  20%  on  the  cost? 

35.  A  merchant  sent  an  agent  $  5114  with  which  to 
buy  goods.  The  agent  was  to  deduct  $14  for  freight, 
and  2%  commission.     What  was  the  value  of  the  goods? 

36.  For  what  must  goods  worth  $1940  be  insured  at 
3  %  so  that  in  case  of  loss  the  value  of  the  goods  and  the 
premium  may  be  recovered? 

37.  A  man  has  an  income  equal  to  20%  of  his  capital. 
He  pays  for  taxes  and  insurance  $150,  which  is  3%  of 
his  income.     What  is  his  capital  ? 

38.  A  sold  B  a  horse,  which  cost  him  $160,  at  121% 
profit.  B  sold  it  to  C  at  a  profit  of  10  % .  What  would 
have  been  A's  per  cent  of  profit  if  he  had  sold  it  to  C 
for  the  price  C  paid  ? 


PERCENTAGE  147 

39.  If  20  gallons  of  water  are  added  to  120  gallons 
of  milk,  what  per  cent  of  the  mixture  is  each  ? 

40.  Find  the  rate  of  gain  or  loss  when  J  of  a  barrel 
of  sugar  is  sold  for  |  of  the  cost  of  a  barrel. 

41.  If  a  house  costs  me  $4000  when  money  is  worth 
8%  and  my  taxes  and  insurance  amount  to  4%,  how 
much  does  the  use  of  the  house  actually  cost  me  each 
year  ? 

42.  Mr.  Jones  insured  his  house  and  furniture  for  | 
of  their  value  at  2%,  and  paid  a  premium  of  $48. 
What  was  the  value  of  each,  if  the  furniture  was  worth 
|  as  much  as  the  house  ? 

43.  A  note  dated  July  15,  1896,  was  paid  Oct.  30, 
1897,  with  8%  interest.  If  the  amount  was  $6620, 
what  was  the  face  of  the  note  ? 

44.  An  insolvent  debtor  was  able  to  pay  70  cents  on 
the  dollar.  He  owed  A  $  6000.  What  was  A's  total  loss, 
if  he  allowed  2%  of  the  debt  for  immediate  payment  ? 

45.  An  article  is  marked  to  gain  40%,  but  the  sales- 
man gives  a  discount  of  10%.  A  collector  is  afterwards 
paid  10%  of  the  debt  for  collecting  it.  What  per  cent 
does  the  merchant  gain  ? 

46.  If  I  ask  for  a  horse  20%  more  than  he  cost  me, 
but  afterwards  make  a  deduction  of  10%  from  my  ask- 
ing price,  and  thus  receive  $162,  how  much  did  the 
horse  cost  me  ? 

47.  A  man  had  a  farm  for  which  he  paid  $  1200.  He 
sold  it  for  $1300,  but  becoming  dissatisfied  with  his  sale 
he  bought  the  farm  back  for  $1500.  What  per  cent  of 
the  first  cost  did  he  lose  by  the  double  transaction  ? 


148  PERCENTAGE 

48.  The  sum  of  10%  of  a  number  and  5%  of  half  the 
remainder  is  what  per  cent  of  a  quarter  of  the  number  ? 

49.  How  much  is  gained  on  a  bicycle  listed  at  $  48, 
bought  at  10%  discount,  and  sold  at  25%  above  the  list 
price  ? 

50.  An  agent  charged  4%  commission  and  $34  ex- 
penses for  selling  a  farm,  and  sent  the  owner  $1166. 
What  was  the  selling  price  of  the  farm  ? 

51.  A  merchant  deducts  20%  from  the  marked  price 
of  his  goods  and  still  makes  a  profit  of  20%.  At  what 
advance  on  the  cost  are  the  goods  marked  ? 

52.  A  and  B  each  invest  $  4000  in  business.  At  the 
end  of  the  year  A  has  gained  5|%,  and  B  has  lost  4|%. 
How  much  has  each  at  the  end  of  the  year  ? 

53.  A  farmer's  crop  of  potatoes  last  year  was  5% 
more  than  it  was  this  year.  How  many  bushels  did  he 
raise  this  year,  if  in  the  two  years  he  raised  615  bushels? 

54.  A  lady's  cloak  cost  $36.  The  making  cost  25% 
less  than  the  cloth,  and  the  trimmings  25%  more  than 
the  cloth.     How  much  did  each  cost  ? 

55.  A  grocer  buys  goods  to  the  amount  of  $  12,000. 
For  how  much  does  he  sell  them  if  he  realizes  20% 
profit,  allowing  4%  of  the  sales  for  bad  debts  ? 

56.  A  merchant  charges  1%  a  month  for  overdue 
accounts.  Mr.  Jones  owes  him  an  account  of  $540 
which  is  8  months  overdue.  How  much  will  Mr.  Jones 
have  to  pay  to  settle  his  account  ? 

57.  My  store  is  valued  at  $  2500,  and  the  goods  at 
$  2000.  If  I  insure  the  whole  for  |  of  their  value  at 
|%,  what  is  my  annual  premium  ? 


PERCENTAGE  149 

58.  A  certain  principal  in  2  years  3  months  and  18 
days  at  6%  amounts  to  $5690.  In  how  many  years 
more  will  it  amount  to  $  6400  ? 

59.  A  man  bought  a  farm  for  $  8000  and  paid  $  3000 
cash,  the  balance  of  the  cost  remaining  on  mortgage 
at  6%.  If  the  net  income  from  the  farm  was  $500 
per  annum,  what  rate  of  interest  did  he  obtain  for  his 
money  ? 

60.  A  man  having  $4800  in  a  bank  drew  out  25%  of 
it  at  one  time,  and  50%  of  the  remainder  at  another, 
and  then  deposited  a  sum  equal  to  120%  of  what  he  had 
drawn  out.     How  much  did  he  then  have  in  the  bank  ? 

61.  A  merchant  began  business  with  a  certain  capital 
which  he  increased  the  first  year  20%  ;  on  this  capital 
he  gained  the  second  year  25%  ;  and  the  third  year  he 
gained  on  the  previous  year  40%,  when  he  was  worth 
$  21,000.     With  what  capital  did  he  begin  ? 

62.  A  miller  had  50  barrels  of  flour  worth  $6  per 
barrel;  but  10  barrels  were  destroyed  by  being  wet. 
How  much  should  he  receive  per  barrel  for  the  remain- 
der to  clear  8%  on  the  cost  of  the  whole  quantity? 

63.  A  widow  received  40%  of  her  husband's  estate, 
and  her  daughter  26%  of  it,  the  widow  securing  $4200 
more  than  the  daughter.  Find  each  one's  share  and  the 
value  of  the  estate. 

64.  An  agent  purchased  $  4000  worth  of  goods  on 
5%  commission.  His  employer  changing  his  business, 
telegraphed  the  agent  to  sell  the  goods.  The  agent 
sold  them  at  5%  less  than  the  first  cost  on  5%  commis- 
sion.    How  much  was  lost  by  the  transaction  ? 


MISCELLANEOUS   PROBLEMS 


67.  1.  If  £  of  A's  money  is  increased  by  §  of  his 
money,  the  sum  is  $5600.     How  much  has  he? 

2.  Of  a  flock  of  sheep,  \  was  sold  at  one  time,  and 
|  of  the  remainder  at  another  time;  there  were  then 
left  50  sheep.     How  many  were  there  at  first? 

3.  If  3£  yards  of  ribbon  cost  30  cents  more  than  2| 
yards,  how  much  did  it  cost  per  yard? 

4.  A  man  has  in  his  cellar  5|  tons  of  coal.  When 
there  are  only  4£  tons  left,  what  part  of  the  coal  has 
been  used? 

5.  Eggs  bought  at  18  cents  per  dozen  are  sold  at  10 
for  25  cents.     How  many  must  be  sold  to  gain  $12? 

6.  If  3  apples  are  worth  2  lemons,  and  3  lemons  are 
worth  2  oranges,  how  many  apples  are  worth  20  oranges? 

7.  If  |  of  a  ton  of  hay  lasts  a  horse  |  a  month,  how 
long  will  1^  tons  last  him? 

8.  When  §  of  f  of  A's  money  is  equal  to  twice  B's, 
how  much  has  each  if  A  has  $5000  more  than  B? 

9.  A  sold  B  |  of  his  land,  and  then  bought  back  i  of 
what  he  had  sold.  What  part  of  the  land  did  each 
then  own? 

150 


MISCELLANEOUS  PROBLEMS  151 

10.  How  far  may  a  man  ride  from  home  on  a  bicycle, 
at  9  miles  per  hour,  and  walk  back  at  3  miles  per  hour, 
so  as  to  be  gone  9  hours? 

11.  When  |  of  a  pound  of  pork  costs  as  much  as  J 
a  pound  of  beef,  how  much  does  each  cost  per  pound  if 
3  pounds  of  pork  and  4  pounds  of  beef  together  cost 
99  cents? 

12.  If  3  men  can  do  a  piece  of  work  in  8  days,  how 
many  men  can  do  it  in  6  days? 

13.  One  pipe  can  fill  a  cistern  in  4  hours,  and  a 
second  pipe  can  fill  it  in  6  hours.  How  long  will  it 
take  both  running  together  to  fill  it? 

14.  A  seamstress  can  make  a  dress  in  3  days,  but 
with  the  assistance  of  her  sister,  she  can  make  it  in  2 
days.  How  long  will  it  take  the  sister  to  make  the 
dress  ? 

15.  What  is  the  value  per  pound  of  a  mixture  of 
coffee  composed  of  6  pounds  at  27  cents  and  2  pounds 
at  19  cents? 

16.  My  clock  gains  5  minutes  an  hour.  It  is  right 
at  noon.  What  is  the  correct  time  when  the  clock 
shows  5  o'clock  in  the  afternoon  of  the  same  day  ? 

17.  If  |  of  a  pound  of  cheese  costs  2  cents  more  than 
J  of  a  pound  of  butter  at  twice  as  much  per  pound,  how 
much  is  paid  for  each  per  pound  ? 

18.  For  every  2  miles  that  I  can  walk,  I  can  go  9 
miles  on  a  bicycle.  In  a  journey  of  60  miles,  I  walk  3 
times  as  long  as  I  ride.  How  many  miles  do  I  travel 
by  bicycle  ?     How  many  miles  do  I  walk  ? 


152  MISCELLANEOUS  PROBLEMS 

19.  A  grocer  bought  some  sweet  and  some  sour 
apples,  40  bushels  in  all,  for  $18.  For  the  sour  ones  he 
paid  50  cents  per  bushel  and  for  the  sweet  ones  30  cents 
per  bushel.  How  many  bushels  of  each  kind  did  he 
buy? 

Solution  :  —  If  they  had  all  been  sour,  they  would  have  cost  $  20. 
This  cost  is  reduced  20  cents  by  each  bushel  of  sweet  apples  bought ; 
the  total  reduction  being  $2,  there  were  therefore  10  bushels  of 
sweet  apples,  and  30  bushels  of  sour  apples.     Therefore,  etc. 

20.  A  drover  bought  20  animals,  consisting  of  sheep 
and  lambs,  for  all  of  which  he  paid  $100.  For  the  sheep 
he  paid  $6  apiece,  and  for  the  lambs  $2  apiece.  How 
many  of  each  were  there  ? 

21.  The  time  worked  by  a  father  and  his  son,  during 
a  certain  month,  amounted  to  30  days,  for  which  their 
total  wages  were  $70.  How  many  days  did  each  work 
if  the  father  received  $  3,  and  the  son  $  1  per  day  ? 

22.  A  merchant  paid  $  340  for  60  barrels  of  flour  of 
two  qualities.  For  the  better  quality  he  paid  $6,  and 
for  the  inferior  $5  per  barrel.  How  many  barrels  of 
each  quality  did  he  buy  ? 

23.  A  farmer  sold  100  turkeys  and  chickens  for  $68, 
receiving  80  cents  each  for  the  turkeys,  and  50  cents  each 
for  the  chickens.     How  many  of  each  were  there  ? 

24.  A  man  employed  a  certain  number  of  men  at 
$2£  per  day,  and  the  same  number  of  boys  at  $|  per 
day.  If  their  daily  pay  amounted  to  $  39,  how  many  of 
each  were  there? 

25.  A  man  agreed  to  work  for  30  days  at  $  4  per  day, 
but  for  each  day  that  he  was  idle  he  was  to  forfeit  $  2. 


MISCELLANEOUS   PROBLEMS  153 

At  the  end  of  the  time  he  received  $90.     How  many 
days  did  he  work  ? 

Suggestion.  —  When  he  was  idle  he  lost  $  6  per  day. 

26.  A  man  agreed  to  work  18  days  at  $3J  a  day,  and 
to  pay  $1J  for  his  board  for  each  day  that  he  was  idle. 
At  the  end  of  the  time  he  received  $43.  How  many 
days  did  he  work  ? 

27.  An  employer  pays  his  workmen  $  2\  a  day.  He 
hires  5  more  men  and  raises  the  wages  of  all  to  $  3.  By 
doing  so,  his  expenses  are  increased  $  25  a  day.  How 
many  workmen  had  he  at  first  ? 

28.  A  contractor,  by  discharging  10  of  his  men,  and 
reducing  the  wages  of  the  rest  from  $  3  to  $  2^  a  day 
reduced  his  expenses  $50  per  day.  How  many  men 
had  he  at  first  ? 

29.  A  farmer  sold  an  equal  quantity  of  wheat  and 
rye.  He  received  60  cents 'a  bushel  for  the  wheat,  and 
40  cents  a  bushel  for  the  rye.  How  many  bushels  of 
each  were  there,  if  the  sum  received  for  wheat  was  $  6 
more  than  the  sum  received  for  rye  ? 

30.  A  lady  expended  50  ^  more  than  J  her  money  in  one 
store,  50  f  more  than  J  the  remainder  in  another  store, 
and  then  had  $1.50  left.     How  much  had  she  at  first  ? 

Solution  :  —  If  at  the  second  store  she  had  expended  only  \  the 
remainder,  she  would  have  had  $  2  left ;  hence  she  had  $  4  left  at 
the  first  store.  If  at  the  first  store  she  had  expended  only  \  her 
money,  she  would  have  had  $  4^  left ;  hence  she  had  $  9  at  first. 

31.  A  boy  lost  5  more  than  J  his  marbles,  and  later 
he  lost  5  more  than  J  the  remainder,  and  then  had  5. 
How  many  had  he  at  first  ? 


154  MISCELLANEOUS   PROBLEMS 

32.  A  poulterer  sold  12  less  than  J  of  his  chickens, 
and  had  72  left.     How  many  had  he  at  first  ? 

33.  A  farmer  sold  5  bushels  more  than  ^  of  his  load 
of  potatoes  to  one  man,  and  10  bushels  more  than  J  of 
the  remainder  to  another  man,  and  then  had  8  bushels 
left.     How  many  bushels  had  he  in  the  load  ? 

34.  A  boy  gave  3  less  than  J  of  his  marbles  to  his 
brother,  and  2  less  than  J  of  the  remainder  to  a  play- 
mate, and  had  16  left.  How  many  marbles  had  he  at 
first? 

35.  I  paid  my  grocer  $  20  more  than  -|  of  what  I 
owed  him,  and  still  owed  him  $40.  How  much  did  I 
owe  him  at  first? 

36.  A  lady  paid  for  a  cloak  $  20  more  than  f  of  her 
money,  and  had  $80  left.  How  much  did  the  cloak 
cost? 

37.  A  girl  cut  from  a  piece  of  ribbon  J  of  a  yard  less 
than  |  of  it,  and  then  had  2  yards  left.  How  much  was 
there  at  first? 

38.  After  30  feet  had  been  broken  from  the  top  of  a 
flagpole,  there  remained  standing  10  feet  more  than  | 
of  the  pole.     How  long  was  it  at  first? 

39.  A  boy  paid  25  cents  less  than  J  his  money  for  a 
pair  of  shoes,  and  25  cents  more  than  J  the  remainder 
for  a  hat,  and  had  75  cents  left.  How  much  had  he  at 
first? 

40.  A  man  paid  me  $20  more  than  f  of  what  he  owed 
me.  Soon  after  he  paid  me  f  of  the  remainder,  but  he 
still  owed  me  $40.     How  much  did  he  owe  me  at  first? 


MISCELLANEOUS   PROBLEMS  155 

41.  What  is  the  rate  of  the  current  of  a  river  if  a 
man  can  row  down  stream  10  miles  an  hour  and  up 
stream  6  miles  an  hour  ? 

Solution  :  —  Going  down  stream  his  rate  is  increased  by  the 
rate  of  the  current ;  returning,  his  rate  is  diminished  by  the  rate 
of  the  current.  Hence,  the  rate  down  exceeds  the  rate  up  by  twice 
the  rate  of  the  current.     Therefore  the  river  runs  2  miles  an  hour. 

42.  How  fast  can  a  man  row  in  still  water,  if  he  can 
row  down  stream  12  miles  an  hour  and  up  stream  6 
miles  an  hour  ? 

43.  A  boatman  whose  rate  down  a  river  was  1^  times 
his  rate  returning  made  a  round  trip  between  two  points 
in  7J  hours.     How  long  was  he  returning  ? 

44.  If  a  man  rides  away  from  home  at  the  rate  of  6 
miles  an  hour  and  returns  at  the  rate  of  3  miles  an  hour, 
how  long  will  he  take  to  go  1  mile  and  return  ? 

45.  How  far  in  7  hours  can  a  man  travel  at  the  rate 
of  8  miles  an  hour,  and  return  at  6  miles  an  hour  ? 

46.  How  far  down  stream  may  one  go  at  the  rate  of 
10  miles  an  hour,  and  return  at  the  rate  of  5  miles  an 
hour,  so  as  to  be  gone  6  hours  ? 

47.  A  man  went  away  from  home  on  a  railroad  train 
at  the  rate  of  20  miles  an  hour,  and  drove  back  at  the 
rate  of  10  miles  an  hour.  How  far  did  he  go  if  he  was 
gone  9  hours  ? 

48.  If  a  man's  rate  in  returning  from  a  trip  is  J  of 
his  rate  going,  what  is  his  rate  per  hour  returning  if  he 
can  go  36  miles  and  back  in  10  hours  ? 

Suggestion  :  —  Since  his  rate  in  returning  is  but  §  of  his  rate 
going,  he  will  require  §  as  much  time  in  returning  as  in  going. 


156  MISCELLANEOUS  PROBLEMS 

49.  A  man  whose  salary  is  1J  times  his  expenses, 
saves  $  3000  in  10  years.     What  is  his  salary  ? 

50.  A  lady  paid  the  same  amount  of  money  for  each 
of  two  pieces  of  dress  goods.  How  much  did  she  pay 
for  them  if  they  were  10  cents  and  15  cents  a  yard 
respectively,  and  there  were  20  yards  in  all? 

51.  Two  pieces  of  meat  weighing  together  20  pounds 
were  each  sold  for  the  same  sum.  What  was  the  weight 
of  each  piece,  if  they  were  worth  12  cents  and  18  cents 
a  pound  respectively  ? 

52.  How  far  may  a  man  ride  in  a  coach  at  the  rate  of 
12 \  miles  per  hour  and  walk  back  at  the  rate  of  3^ 
miles  per  hour,  and  be  gone  9 \  hours  ? 

53.  A  steamer  goes  down  a  river  at  the  rate  of  12 
miles  an  hour  and  returns  at  the  rate  of  8  miles  an 
hour.  How  far  does.it  go,  if  the  time  going  is  2|  hours 
less  than  the  time  returning  ? 

54.  A  man  drove  to  town  at  the  rate  of  8^  miles  per 
hour,  attended  to  business  that  occupied  him  1|  hours, 
then  drove  home  at  the  rate  of  5  miles  per  hour,  and 
reached  home  after  an  absence  of  7  hours.  How  far 
from  town  did  he  live  ? 

55.  A  farm-hand  agreed  to  work  a  year  for  $300  and 
a  watch.  At  the  end  of  8  months  he  received  as  an 
equitable  settlement  $180  and  the  watch.  How  much 
was  the  watch  worth? 

Solution:  —  In  8  months,  or  f  of  a  year,  he  had  earned  $200 
and  §  of  the  value  of  the  watch.  Since  he  received  but  $180  and 
the  watch,  he  allowed  $20  for  the  other  third  of  its  value.  Hence 
its  value  was  $60.     Therefore,  etc. 


MISCELLANEOUS  PROBLEMS  157 

56.  A  man  agreed  to  work  a  year  for  $400  and  a 
horse.  At  the  end  of  9  months  he  received  $  260  and 
the  horse.     What  was  the  value  of  the  horse  ? 

57.  A  father  and  his  son  were  to  receive  $600  for  a 
year's  work.  At  the  end  of  10  months  the  son  left.  At 
the  end  of  the  year  the  father  received  only  $575.  At 
what  rate  per  year  was  each  paid  ? 

58.  A  man  agreed  to  work  a  year  for  $720  and  48 
bushels  of  wheat.  At  the  end  of  9J  months  he  received 
$540  and  68  bushels  of  wheat.  How  much  was  the 
wheat  worth  per  bushel  ? 

59.  A  man's  work  for  a  year  was  to  be  paid  for  with 
$800  and  100  bushels  of  potatoes.  At  the  end  of  9 
months  he  got  $  620  and  50  bushels  of  potatoes.  What 
was  the  value  of  the  potatoes  per  bushel  ? 

60.  A  hare  is  27  leaps  ahead  of  a  hound,  and  takes 
8  leaps  while  the  hound  takes  5 ;  but  2  of  the  hound's 
leaps  are  equal  to  5  of  the  hare's.  How  many  leaps 
must  the  hound  take  to  catch  the  hare  ? 

Solution: — If  2  of  the  hound's  leaps  are  equal  to  5  of  the 
hare's,  1  of  the  hound's  leaps  equals  f  of  the  hare's,  and  5  of  the 
hound's  equal  12i  of  the  hare's.  Then,  in  taking  5  leaps  the  hound 
gains  4J  of  the  hare's  leaps,  and  to  gain  27  the  hound  must  take  as 
many  times  5  leaps  as  4J  is  contained  times  in  27,  or  6  times  5 
leaps,  which  is  30  leaps.     Therefore,  etc. 

61.  A  is  12  steps  ahead  of  B,  and  takes  4  steps  while 
B  takes  3;  but  2  of  B's  steps  are  equal  to  3  of  A's. 
How  many  steps  must  B  take  to  overtake  A  ? 

62.  A  is  8  steps  ahead  of  B,  and  goes  5  steps  to  B's 
4 ;  but  3  of  B's  are  equal  to  4  of  A's.  How  many  steps 
must  B  take  to  overtake  A  ? 


158  MISCELLANEOUS   PROBLEMS 

63.  A  thief  is  20  steps  ahead  of  an  officer,  and  takes 

6  steps  while  the  officer  takes  5 ;  but  3  of  the  officer's 
steps  are  equal  to  4  of  the  thief's.  In  how  many  steps 
can  the  officer  catch  him? 

64.  If  3  men  and  4  boys  earn  1 13  in  a  day,  and  4 
men  and  3  boys  earn  $15  in  a  day,  what  is  the  daily 
pay  of  a  man  and  of  a  boy? 

Solution  :  —  From  the  first  statement  in  the  problem  it  is  evi- 
dent that  12  men  and  16  boys  can  earn  $52  in  a  day;  from  the 
second,  that  12  men  and  9  boys  can  earn  $45  in  a  day.     Hence, 

7  boys  earn  $  7,  or  $  1  each  per  day.  If  3  men  with  4  boys  at  $  1 
per  day  earn  $  13,  3  men  earn  $  9,  or  each  man  earns  $  3  per  day. 
Therefore,  etc. 

65.  If  2  bushels  of  onions  and  3  bushels  of  potatoes 
cost  $  12,  and  if  3  bushels  of  onions  and  4  bushels  of 
potatoes  cost  $17,  how  much  does  each  cost  per  bushel? 

66.  If  \  of  A's  weekly  wages  and  all  of  B's  amount 
to  $17,  and  if  all  of  A's  and  \  of  B's  amount  to  $16, 
how  much  does  each  get  per  week  ? 

67.  A  boy  works  5  days,  and  his  sister  works  4  days, 
and  together  they  earn  $6.  How  much  does  each  earn 
per  day,  if  together  they  earn  $1.30  a  day? 

68.  At  what  time  between  3  and  4  o'clock  are  the 
hour  and  the  minute  hands  of  a  clock  together  ? 

Solution  :  —  When  it  is  3  o'clock  the  hour  and  minute  hands 
are  15  minute  spaces  apart,  and  the  minute  hand  must  gain  15  min- 
ute spaces  to  overtake  the  hour  hand.  The  minute  hand  gains  on 
the  hour  hand  11  spaces  in  every  12  passed  over,  hence  to  gain 
1  space  it  must  move  \\  spaces,  and  to  gain  15  spaces  it  must  pass 
over  15  times  |f  spaces,  or  \8T°-  spaces,  or  16T4T  spaces.  Hence  they 
are  together  at  16T^  minutes  after  3. 


MISCELLANEOUS  PROBLEMS  159 

69.  At  what  time  between  1  and  2  o'clock  are  the 
hands  of  a  clock  together  ? 

70.  Between  4  and  5  o'clock  the  hands  of  a  clock  are 
together.     What  time  is  it? 

71.  At  4  o'clock  the  minute  hand  is  20  minute  spaces 
behind  the  hour  hand.  When  will  it  be  20  minute 
spaces  ahead  of  the  hour  hand? 

72.  At  what  time  after  8  o'clock  will  the  minute 
and  hour  hands  of  a  clock  first  be  together? 

73.  A  and  B  walk  in  the  same  direction  around  a 
track  100  rods  in  circumference,  A  going  5  rods  while 
B  goes  3  rods.  When  A  starts  B  is  20  rods  ahead. 
How  far  from  the  starting  point  will  A  overtake  B  ? 

74.  At  what  time  between  3  and  4  o'clock  are  the 
hands  of  a  clock  opposite  ? 

75.  What  time  is  it  if  ^  of  the  time  past  noon  is 
equal  to  ^  of  the  time  to  midnight  ? 

Solution  :  —  If  I  of  the  time  past  noon  is  equal  to  }  of  the  time 
to  midnight,  the  time  past  noon  is  equal  to  f  of  the  time  to  mid- 
night, and  |  of  the  time  to  midnight  equals  the  time  from  noon  to 
midnight,  which  is  12  hours ;  consequently  ^  of  the  time  to  mid- 
night is  |  hours,  and  the  time  to  midnight  is  *f»  hours,  equal  to 
1\  hours.  Therefore  the  time  past  noon  equals  12  hours  less  7| 
hours,  or  4J  hours,  hence  the  time  is  half  past  4  o'clock. 

76.  If  \  of  the  time  past  noon  is  equal  to  \  of  the 
time  to  midnight,  what  time  is  it? 

77.  What  time  is  it  if  \  of  the  time  past  noon  is 
equal  to  \  of  the  time  to  midnight? 

78.  What  time  is  it  if  \  of  the  time  since  9  o'clock  in 
the  morning  is  equal  to  \  of  the  time  to  midnight? 


160  MISCELLANEOUS  PROBLEMS 

79.  I  have  horses  and  cows  to  the  number  of  60,  20 
of  which  are  cows.  How  many  more  horses  must  I  buy 
so  that  there  may  be  5  horses  to  2  cows  ? 

Solution  :  —  There  are  10  times  2  cows,  and  to  keep  the  rate  of 
5  horses  to  2  cows  there  should  be  10  times  5  horses.  But  there 
are  only  40 ;  consequently  10  more  horses  should  be  bought. 

80.  If  100  pounds  of  sea  water  contain  5  pounds  of 
salt,  how  much  fresh  water  must  be  added  that  50 
pounds  of  the  new  mixture  shall  contain  2  pounds  of 
salt? 

81.  In  100  drops  of  prussic  acid  as  prepared  for 
medical  use,  there  are  only  2  drops  of  the  pure  acid. 
How  many  drops  of  the  mixture  are  there  in  a  dose 
containing  -^  of  a  drop  of  the  pure  acid  ? 

82.  In  160  pounds  of  a  certain  brand  of  solder  there 
are  60  pounds  of  tin,  and  the  rest  is  lead.  How  much 
tin  must  be  added  that  the  mixture  may  be  %  tin  ? 

Suggestion  :  —  The  new  mixture  will  contain  4  pounds  of  tin 
to  5  pounds  of  lead. 

83.  In  a  class  of  72  pupils  30  of  them  are  boys. 
How  many  girls  must  leave  so  that  there  may  be  4 
girls  to  5  boys? 

84.  A  farmer  has  120  sheep  and  cows,  the  cows  being 
f  as  many  as  the  sheep.  How  many  sheep  must  he 
buy  that  he  may  have  9  sheep  to  5  cows  ? 

85.  In  a  mixture  of  60  ounces  of  silver  and  copper 
there  are  4  ounces  of  silver.  How  much  copper  must 
be  added  that  10  ounces  of  the  new  mixture  shall  con- 
tain |  of  an  ounce  of  silver  ? 


MISCELLANEOUS  PROBLEMS  161 

86.  A  man  spends  $  1G0  for  an  equal  number  of  sheep 
and  lambs-,  paying  $5  each  for  the  sheep  and  $3  each 
for  the  lambs.  How  many  lambs  must  he  sell  that 
there  shall  be  |  as  many  lambs  as  sheep  ? 

87.  A  having  $ 150  in  a  bank  drew  out  and  put  into 
his  purse  as  much  as  it  already  contained.  He  then 
had  equal  sums  in  each.     How  much  did  he  draw  out  ? 

88.  A  had  $140  and  lent  B  |  as  much  as  B  already 
had,  and  then  each  had  the  same  sum.  How  much  had 
B  at  first  ? 

89.  A  has  a  farm  of  250  acres  and  sells  B  -|  as  many 
acres  as  B  already  has.  B  then  has  \  as  much  as  A. 
How  much  has  each  after  the  sale  ? 

90.  Anna  is  21  years  old,  and  her  niece  is  9.  How 
long  is  it  since  Anna  was  3  times  as  old  as  her  niece  ? 

Solution  :  —  When  Anna  was  3  times  as  old  as  her  niece,  the 
difference  between  their  ages  was  twice  the  niece's  age.  But  since 
this  difference,  12  years,  is  always  the  same,  twice  the  niece's  age 
at  the  required  time  was  12  years,  and  her  age  was  6  years ;  hence, 
Anna  was  3  times  as  old  as  her  niece  3  years  ago. 

91.  John  is  8  years  old,  and  his  father  32.  How 
many  years  old  will  each  be  when  John's  age  is  \  of 
his  father's  age  ? 

92.  My  age  is  60  years,  and  that  of  my  oldest  son  is 
30  years.     How  long  ago  was  I  3  times  as  old  as  he  ? 

93.  A  steamer  goes  5  miles  down  stream  in  the  same 
time  that  it  goes  3  miles  up  stream ;  but  if  its  rate  each 
way  is  diminished  4  miles  an  hour,  its  rate  down  stream 
will  be  twice  its  rate  up  stream.  How  fast  does  it  go 
in  each  direction  ? 

MILNE    MENTAL  —  11 


162  MISCELLANEOUS   PROBLEMS 

94.  At  3  o'clock  the  minute  hand  is  15  minute  spaces 
behind  the  hour  hand.  How  long  afterward  will  it  be 
15  minute  spaces  ahead  of  the  hour  hand  ? 

95.  If  2|  quarts  of  vinegar  cost  19  cents,  how  much 
will  2|  gallons  cost? 

96.  If  1£  bushels  of  cranberries  cost  $1.68,  how 
much  will  1J  pecks  cost? 

97.  The  labor  of  4  boys  is  worth  as  much  as  that  of 

2  men.    When  a  man  can  earn  $3  a  day,  how  much  can 

3  boys  and  4  men  earn  in  6  days  ? 

98.  The  head  of  a  fish  is  §  as  long  as  the  tail,  and  the 
body  is  3  times  as  long  as  the  head  and  tail  together. 
How  long  is  each,  if  the  fish  is  56  inches  in  length  ? 

99.  When  wheat  flour  is  worth  3  times  as  much  as 
rye  flour,  a  baker  gets  10  cents  for  a  loaf  of  bread  £  rye. 
How  much  should  he  get  when  a  loaf  of  the  same  weight 
is  half  rye  ? 

100.  Two  boys  on  a  fishing  excursion  take  8  sand- 
wiches for  their  lunch,  one  furnishing  5  and  the  other 
3.  A  third  boy  joins  them,  paying  16  cents  for  an 
equal  share  of  the  lunch.  How  much  of  the  money 
should  each  of  the  two  boys  have  ? 

101.  A's  money  is  1^  times  B's,  and  C  has  |  as  much 
as  A  and  B  together.  How  much  has  each,  if  all  their 
money  is  $180? 

102.  When  §  of  the  time  past  noon  is  equal  to  the 
time  to  midnight,  what  time  is  it? 

103.  After  5  men  have  worked  6  days  at  a  piece  of 
work,  they  are  joined  by  7  other  men,  with  whose  help 


MISCELLANEOUS  PROBLEMS  163 

the  work  is  finished  in  5  days  more.     How  long  would 
it  have  taken  the  5  men  to  do  the  entire  work  ? 

104.  A  man  bought  some  sheep  at  $5  each.  Reserving 
10,  he  sold  the  remainder  at  a  gain  of  $  2  per  head,  and 
received  for  them  $10  more  than  they  all  cost.  How 
many  sheep  were  there  ? 

105.  A  and  B  agreed  to  plow  a  field  for  $120.  A 
plowed  *-  of  the  field  and  5  acres  besides  and  received 
$  50.     How  many  acres  were  there  ? 

106.  A  and  B  agree  to  cut  94  cords  of  wood.  How 
many  cords  does  each  cut,  if  J  of  what  A  cuts  is  2  cords 
more  than  |  of  what  B  cuts  ? 

107.  Two  men  hired  a  pasture  for  $42.  A  put  in  5 
horses  for  4  weeks,  and  B  put  in  12  horses  for  3  weeks. 
How  much  should  each  pay  ? 

108.  If  a  man  can  do  |  of  a  piece  of  work  in  18  days, 
in  what  time  can  3  men  do  the  entire  work  ? 

109.  A  and  B  can  do  a  piece  of  work  in  3  days ;  A 
and  C,  in  4  days  ;  B  and  C,  in  6  days.  How  long  will 
it  take  each  alone,  and  how  long  all  together  to  do  it  ? 

110.  The  interest  on  a  certain  principal  for  5  years 
at  4%  is  a  sum  such  that  in  5  years  at  6%  the  interest 
on  it  will  be  $150.     Find  the  original  principal. 

111.  A  is  50  rods  ahead  of  B,  and  goes  3  rods  while 
B  goes  5.     How  far  must  B  go  to  overtake  A  ? 

112.  A,  who  goes  3  miles  an  hour,  and  B,  who  goes 
4,  start  from  the  same  point  and  travel  in  the  same 
direction  around  an  island  72  miles  in  circumference. 
How  far  will  each  travel  before  they  are  together  ? 


164  MISCELLANEOUS   PROBLEMS 

113.  George  has  70  cents  more  than  Charles,  and  § 
of  George's  money  is  equal  to  |  of  Charles's  money. 
How  much  has  each  ? 

114.  Apples  bought  at  2  cents  for  3  are  sold  at  3 
cents  for  2.     What  is  the  gain  per  cent  ? 

115.  A  rope  33  ft.  long  is  cut  so  that  §  of  one  piece  is 
6  ft.  less  than  |  of  the  other.     How  long  is  each  piece  ? 

116.  If  3  men  and  5  boys  earn  $  110  in  a  week,  and  5 
men  and  3  boys  $130  in  a  week,  what  are  the  wages 
per  week  of  a  man  and  of  a  boy  ? 

117.  The  interest  for  5  years,  at  4%,  of  A's  and  B's 
money  together  is  $  280.  How  much  has  each,  if  §  of 
A's  money  is  equal  to  i  of  B's  ? 

118.  A,  B,  and  C  together  did  a  piece  of  work  for 
$84.  They  agreed  to  divide  the  money  so  that  A 
should  have  $5  as  often  as  B  had  14  and  C$3.  How 
much  did  each  get  ? 

119.  How  much  must  be  paid  for  12  melons  if  5 
melons  are  worth  12  peaches,  and  5  peaches  are  worth 
25  cents  ? 

120.  A  steamer  goes  12  miles  an  hour  down  stream 
and  10  miles  an  hour  up  stream.  How  far  down  stream 
can  it  go  and  be  back  10  hours  from  the  time  it  left  ? 

121.  A's  money  and  §  of  B's  amounts  to  $  8000.  How 
much  has  each  if  |  of  A's  is  equal  to  J  of  B's  ? 

122.  How  far  may  one  go  in  a  car  that  runs  12  miles 
per  hour,  that  he  may  walk  back  at  the  rate  of  3  miles 
per  hour,  and  be  gone  only  10  hours  ? 


MISCELLANEOUS   PROBLEMS  165 

123.  If  sea  water  contains  5%  of  salt,  how  many 
pounds  of  fresh  water  must  be  added  to  100  pounds  of 
sea  water,  so  that  the  mixture  may  contain  4%  of  salt  ? 

124.  I  paid  a  debt  of  $4f  with  dimes  and  25-cent 
pieces.  How  many  of  each  kind  of  coin  were  there,  if 
|-  the  number  of  dimes  was  equal  to  f  the  number  of 
25-cent  pieces  ? 

125.  In  a  mixture  of  silver  and  copper  weighing  80 
ounces,  there  are  8  ounces  of  copper.  How  many 
ounces  of  silver  must  be  added  that  the  mixture  may 
be  5%  copper? 

126.  A  tree  137  feet  long  was  broken  into  two  pieces 
such  that  |  of  the  shorter  piece  was  10  feet  shorter 
than  |  of  the  longer.     How  long  were  the  pieces? 

127.  If  I  pay  my  grocer's  bill  and  half  my  butcher's 
bill,  it  will  take  $  60 ;  if  I  pay  half  my  grocer's  bill  and 
half  my  butcher's  bill,  it  will  take  $48.  How  much  do 
I  owe  each  ? 

128.  I  gain  20%  after  giving  a  discount  of  25%  and 
20%  from  the  list  price  of  a  piano.  What  was  the  list 
price,  if  the  piano  cost  me  $  300  ? 

129.  A  man  earns  $5  per  day,  and  pays  $1J  per  day 
for  his  board.  At  the  end  of  60  days  he  has  saved 
$  160.     How  many  days  has  he  been  idle  ? 

130.  A,  B,  and  C  can  do  a  piece  of  work  in  If  days; 
A  and  B  can  do  it  in  2^  days;  and  B  can  do  it  in  5  days. 
How  long  will  it  take  each  to  do  it  ? 

131.  Two  men  or  5  boys  can  do  a  piece  of  work  in  12 
days.     How  long  will  it  take  4  men  and  2  boys  to  do  it  ? 


166  MISCELLANEOUS   PROBLEMS 

132.  One  half  of  A's  money  plus  £  of  B's  =  I 
and  ^  of  A's  plus  £  of  B's  =  $  60.     How  much  has  each  ? 

133.  Arthur  and  Louis  together  have  80  marbles ; 
|  of  Arthur's  marbles  increased  by  8  are  equal  to  |  the 
number  Louis  has.     How  many  has  each  ? 

134.  Divide  100  into  two  parts,  such  that  7  times  the 
first  part  shall  be  equal  to  3  times  the  second  part. 

135.  When  I  divide  a  certain  number  by  8,  the  re- 
mainder is  3;  what  is  the  number  if  the  quotient  is 
twice  the  remainder  ? 

136.  A  boy  bought  65  oranges  and  lemons.  How 
many  of  each  were  there,  if  5  times  the  number  of 
oranges  was  equal  to  1|  times  the  number  of  lemons? 

137.  The  amount  of  a  certain  principal  for  a  certain 
time  at  4%  is  1480,  and  at  7%  it  is  $540.  Find  the 
principal  and  the  time. 

138.  By  advancing  the  price  of  a  piano  $22,  the  gain 
is  increased  2f  %.     Find  the  cost  of  the  piano. 

139.  John  is  22  years  old,  and  his  father  46.  How 
long  ago  was  John's  age  J  of  his  father's  age  ? 

140.  A  certain  number  of  oxen  cost  $1800.  A  later 
purchase  of  5  oxen  at  $10  less  each  made  the  entire 
cost  $2050.     How  many  were  bought  the  first  time? 

141.  The  sum  of  two  numbers  is  40,  and  their  differ- 
ence multiplied  by  itself  is  100.  What  are  the  num- 
bers ? 

142.  A  has  2 \  times  as  much  money  as  B,  but  after  B 
has  borrowed  30  cents  from  A,  they  have  equal  amounts. 
How  much  had  each  at  first  ? 


MISCELLANEOUS   PROBLEMS  167 

143.  A  father  takes  3  steps  while  his  son  takes  5,  but 
2  of  the  father's  steps  are  equal  to  3  of  the  son's.  How 
many  steps  will  the  son  require  to  overtake  the  father, 
who  is  24  steps  ahead? 

144.  Divide  $66  among  A,  B,  and  C,  so  that  A  shall 
have  40  cents  as  often  as  B  has  50  cents  and  C  75 
cents. 

145.  A  man  sells  two  stoves  at  $40  each,  gaining 
331%  on  one,  and  losing  331%  0n  the  other.  What 
per  cent  does  he  gain  or  lose  on  both? 

146.  The  head  of  a  fish  is  6  inches  long ;  the  tail  is 
twice  as  long  as  the  head,  and  the  body  is  as  long  as  the 
head  and  tail  together.     How  long  is  the  fish  ? 

147.  A  clock  gains  10  seconds  in  5  minutes.  On  Mon- 
day at  noon  it  is  set  right.  What  is  the  correct  time 
when  the  clock  indicates  noon  on  Tuesday? 

148.  Three  pedestrians  whose  rates  are  as  the  num- 
bers 3,  4,  and  5  start  from  the  same  point  to  walk  in  the 
same  direction  around  a  circular  track  120  yards  in  cir- 
cumference. They  are  together  at  the  start ;  when  are 
they  next  together,  and  how  far  has  each  gone  ? 

149.  A  tree  in  falling  is  broken  into  3  pieces.  The 
lower  piece  is  f  as  long  as  the  middle  piece,  and  |  of  the 
length  of  the  top  is  1|  times  the  length  of  the  middle. 
How  long  is  each  piece  if  the  tree  is  170  feet  high? 

150.  What  part  of  10  is  80%  of  8£?  What  %  of 
10  is  80%  of  7J? 

151.  A  cistern  can  be  filled  by  one  pipe  in  20  minutes, 
by  another  in  30  minutes,  and  a  third  pipe  can  empty 


168  MISCELLANEOUS  PROBLEMS 

it  in  15  minutes.     If  it  is  empty,  and  all  run  together, 
in  how  many  minutes  will  it  be  filled  ? 

152.  If  20%  of  the  cost  of  a  horse  is  equal  to  30%  of 
the  cost  of  a  wagon,  what  must  be  the  selling  price  of  each 
to  gain  25%  if  the  horse  cost  $100  more  than  the  wagon? 

153.  By  raising  the  price  of  flour  50  cents  a  barrel,  a 
grocer  increases  his  gain  from  20%  to  25%.  What  does 
the  flour  cost  him,  and  what  does  he  get  for  it  ? 

154.  A  man  bought  40  yards  of  silk  at  $4  a  yard. 
After  10%  of  it  was  ruined  by  accident  he  sold  the 
remainder  so  as  to  gain  12|%  on  the  cost  of  the  whole. 
What  was  the  selling  price  per  yard  ? 

155.  Mary  spent  5  cents  more  than  £  of  her  money  for 
ribbons ;  5  cents  more  than  ^  the  remainder  for  a  doll ; 
5  cents  more  than  £  of  what  still  remained  for  a  book. 
She  then  had  25  cents  left.    How  much  had  she  at  first  ? 

156.  If  the  shorter  piece  of  a  broken  pole  that  was 
90  feet  long  is  diminished  by  6  feet,  its  length  will  be  J 
that  of  the  longer  piece.     How  long  is  each  piece  ? 

157.  If  a  baker  charges  8  cents  for  a  5-ounce  loaf,  how 
much  should  he  charge  for  an  8-ounce  loaf  when  flour 
is  1^  times  as  dear? 

158.  Twelve  men  charter  a  car  to  go  on  an  excursion. 
By  taking  in  8  more,  the  expense  is  diminished  $  2  for 
each  man.     How  much  is  paid  for  the  car? 

159.  Twenty-five  men  engage  a  dinner,  but  when  the 
dinner  is  served,  5  of  them  are  absent,  by  which  the 
expense  is  increased  $1  for  each  man.  How  much  do 
they  pay  in  all  ? 


MISCELLANEOUS  PROBLEMS  169 

160.  The  distance  around  a  rectangular  field  whose 
length  is  to  its  breadth  as  5  to  3  is  640  rods.  How  many 
acres  are  there  in  the  field  ? 

161.  A  loaned  B  $800  for  4|  months.  How  long 
should  B  loan  A  $600  to  discharge  the  obligation? 

162.  A  train  runs  72  miles  in  2  hours  and  40  minutes. 
What  is  the  rate  per  hour? 

163.  In  a  certain  school  there  are  100  pupils,  40  of 
whom  are  girls.  How  many  girls  must  leave  the  school 
so  that  80%  of  the  pupils  may  be  boys? 

164.  If  I  buy  new  oats  for  30  cents  per  bushel,  and 
they  shrink  10%  in  drying,  how  much  per  bushel  should 
I  charge  for  them  to  make  a  profit  of  20%  ? 

165.  A  man  gave  money  to  some  children,  giving 
10  cents  to  each,  and  had  10  cents  left.  If  he  had 
given  12  cents  to  each,  he  would  have  lacked  8  cents 
of  having  enough  money.  How  much  money  had  he, 
and  how  many  children  were  there  ? 

166.  A  man  paid  a  debt  of  $6.20  with  32  coins, 
viz.,  quarters  and  dimes.  The  quarters  were  If  times 
the  dimes  in  number.     How  many  of  each  were  there  ? 

167.  A  man  receives  $  3  a  day  and  his  board  when  he 
works,  but  when  he  is  idle  he  pays  $1J  a  day  for  his 
board.  At  the  end  of  40  days  he  receives  $  75.  How 
many  days  has  he  been  idle  ? 

168.  A  and  B  can  do  a  piece  of  work  in  6  days ;  A 
and  C  can  do  it  in  8  days  ;  B  and  C  can  do  it  in  12  days. 
How  long  will  it  take  the  three  together  to  do  it,  and 
how  long  each  one  separately  ? 


170  MISCELLANEOUS  PROBLEMS 

169.  A  man  burns  3|  tons  of  coal  in  2|  months. 
How  much  at  $5  per  ton  will  his  coal  cost  for  a  year  at 
that  rate  ? 

170.  If  the  square  of  a  certain  number  is  increased 
by  25  the  square  root  of  the  result  is  13.  What  is 
the  number? 

171.  A  man  pays  $264  for  a  number  of  sheep  at  $8 
each,  and  2\  times  as  many  hogs  at  $10  each.  How 
many  of  each  does  he  buy  ? 

172.  If  |  of  A's  money  increased  by  $10  is  equal  to 
|  of  B's  increased  by  $18,  how  much  has  each,  if  they 
have  together  $182? 

173.  A  man  paid  $120  for  some  sheep  and  lambs. 
By  selling  them  all  at  $  2 \  each,  he  gained  $  5.  How 
many  of  each  were  there,  if  the  lambs  were  1J  times  as 
many  as  the  sheep  ? 

174.  When  raspberries  are  worth  |  as  much  as 
strawberries,  a  quart  and  a  pint  of  each  cost  45  cents. 
How  much  is  each  per  quart? 

175.  Two  children,  at  the  ages  of  13  and  15  years 
respectively,  inherit  $2700,  which  is  to  be  divided  so 
that  the  shares  of  both  put  at  simple  interest  at  5%  will 
amount  to  equal  sums  when  each  is  21  years  old.  What 
is  the  share  of  each? 

176.  If  I  pay  4  cents  a  pound  less  for  meat,  12  pounds 
can  be  bought  for  what  8  pounds  would  have  cost. 
What  is  the  higher  price? 

177.  A  boy  leaves  home  on  his  bicycle,  and  travels 
at  the  rate  of   8  miles  per  hour.     His  bicycle  breaks 


MISCELLANEOUS   PROBLEMS  171 

down,  and  he  walks  home  at  the  rate  of  3  miles  per 
hour.  How  far  from  home  was  he,  if  he  was  absent  11 
hours  ? 

178.  A  certain  principal  at  5%  simple  interest  yields, 
in  a  certain  time,  interest  equal  to  5  times  the  principal. 
Find  the  time. 

179.  If  the  interest  on  a  certain  sum  of  money  for  8 
years  at  5%  is  placed  at  interest  for  the  same  time,  and 
at  the  same  rate,  it  will  yield  1 40  interest.  What  is 
the  first  principal? 

180.  If  the  sides  of  a  square  are  increased  by  4  feet, 
its  area  will  be  80  square  feet  greater.  Find  the  side 
of  the  original  square. 

181.  A  drover  bought  some  sheep  at  $5  each.  After 
4  of  them  had  died,  he  sold  the  remainder  at  $6  per 
head,  and  received  for  them  what  all  the  sheep  cost. 
How  many  did  he  buy  ? 

182.  A  man  who  can  walk  3  miles  an  hour  up  hill, 
and  4  miles  an  hour  down  hill,  requires  17  hours  to 
make  a  journey  of  60  miles.  How  much  of  the  road  is 
up  hill,  and  how  much  down  hill  ? 

183.  Disregarding  the  resistance  of  the  air,  an  object 
falls  16^  feet  the  first  second,  3  times  that  distance  the 
second  second,  5  times  that  distance  the  third  second, 
and  so  on.  How  far  does  it  fall  in  2  seconds?  in  3 
seconds?  in  5  seconds?  in  6  seconds? 

184.  How  much  farther  does  a  body  fall  the  5th 
second  than  the  3d?  the  7th  than  the  4th?  How 
far  will  it  fall  in  10  seconds? 


172  MISCELLANEOUS  PROBLEMS 

185.  A  merchant  bought  a  certain  number  of  yards 
of  cloth  at  $1  for  5  yards,  and  the  same  number  of 
yards  at  $  1  for  4  yards.  He  sold  it  all  at  the  rate  of 
$2  for  9  yards,  and  lost  $1.  How  many  yards  did  he 
buy? 

186.  A  customer  bought  what  he  supposed  was  $45 
worth  of  sugar,  but  a  false  weight  having  been  used  he 
got  only  $40  worth.  How  many  ounces  were  given 
him  for  a  pound  ? 

187.  If  1  sell  one  of  my  two  houses  for  $4500  and 
the  other  for  $  1860,  I  will  gain  6  %  on  the  cost  of 
both  ;  but  if  I  sell  the  dearer  house  at  $4000  and  the 
other  at  cost,  I  will  lose  5%.  What  was  the  cost  of 
each  house  ? 

188.  A  farmer  has  434  bushels  of  wheat  in  3  bins. 
Two  thirds  of  the  number  of  bushels  in  the  first  bin 
equals  |  of  the  number  in  the  second,  and  |  of  the 
number  in  the  second  equals  |  the  number  in  the  third. 
How  many  bushels  of  wheat  are  there  in  each  bin  ? 

189.  A  commission  merchant  who  charged  5%,  both 
for  selling  and  for  buying,  received  $1500  worth  of 
produce  and  $675  in  cash,  with  instructions  to  sell  the 
produce  and  to  invest  the  whole  in  flour  at  $5  per 
barrel.     How  many  barrels  of  flour  were  purchased  ? 

190.  A  merchant's  expenses  during  a  certain  year 
were  33^%  of  the  gross  gain  on  his  sales.  His  goods 
were  marked  30%  above  cost.  At  the  beginning  of 
the  next  year  he  advanced  the  price  of  his  goods  10% 
of  the  marked  price,  and  during  the  year  cut  down  his 
expenses  10%.  What  per  cent  did  he  gain  during  the 
second  year  ? 


TABLES   OF  DENOMINATE  NUMBERS 


68. 


LINEAR  MEASURE 

Table 

12  Inches  (in.)         =  1  Foot     .     .     . 

.    ft. 

3  Feet                     =  1  Yard    .     .     . 

.   yd. 

5}  Yards  or  16J  ft.  =  1  Rod      .     .     . 

.    rd. 

320  Rods                    =  1  Mile     .     .    . 

.    mi. 

The  following  are  also  used : 

3  Barleycorns  =  1  Inch.     Used  by  shoemakers. 

4  Inches 
6  Feet 
3  Feet 

5  Paces 
8  Furlongs 


=  1  Hand.     Used  to  measure  the  height  of  horses. 

=  1  Fathom.     Used  to  measure  depths  at  sea. 

=  1  Pace.^ 

—  1  T?  A    \     Used  in  pacing  distances. 

=  1  Mile. 


SQUARE  MEASURE 

Table 

144  Square  Inches  (sq.  in.)=  1  Square  Foot 
9  Square  Feet  =  1  Square  Yard 

30J  Square  Yards  =  1  Square  Rod 

160  Square  Rods  =  1  Acre  .     .     . 

640  Acres  =  1  Square  Mile 

173 


sq.  ft. 
sq.  yd. 
sq.  rd. 
A. 


sq.  mi. 


174  TABLES  OF   DENOMINATE   NUMBERS 

CUBIC   MEASURE 

Table 

1728  Cubic  Inches  (cu.  in.)=  1  Cubic  Foot     .     .     .     cu.  ft. 
27  Cubic  Feet                     =  1  Cubic  Yard    .     .     .     cu.  yd. 
128  Cubic  Feet  =  1  Cord C. 

A  cord  of  wood  or  stone  is  a  pile  8  ft.  long,  4  ft.  wide,  and  4  ft. 
high. 

LIQUID  MEASURE 

Table 

4  Gills  (gi.)=l  Pint  .  .  .  .  pt. 
2  Pints  =  1  Quart .  .  .  .  qt. 
4  Quarts       =  1  Gallon     .     .     .     gal. 

DRY  MEASURE 

Table 

2  Pints  (pt.)  =  1  Quart  .  .  .  .  qt. 
8  Quarts  =  1  Peck  .  .  .  .  pk. 
4  Pecks  ss  1  Bushel  ....    bu. 

AVOIRDUPOIS  WEIGHT 

Table 

16  Ounces  (oz.)       =  1  Pound lb. 

100  Pounds                 =  1  Hundredweight   .     .     cwt- 
20  Hundredweight  =  1  Ton T. 

TROY  WEIGHT 

Table 

24  Grains  (gr.)     =  1  Pennyweight    .     .     .     pwt. 

20  Pennyweights  =  1  Ounce oz. 

12  Ounces  =  1  Pound lb. 


TABLES  OF   DENOMINATE  NUMBERS 


175 


TIME 

Table 

60  Seconds  (sec 

.)  =  1  Minute     . 

.     .    min 

60  Minutes 

=  1  Hour  .     . 

.     .    hr. 

24  Hours 

=  lDay     .     . 

.     .     da. 

7  Days 

=  1  Week  .     . 

.     .     wk. 

365  Days 

=  1  Year   .     . 

.     .     yr. 

366  Days 

=  1  Leap  Year 

.     .     yr. 

100  Years 

=  1  Century  . 

.     .     cen. 

Centennial  years  exactly  divisible  by  400,  and  other  years  exactly 
divisible  by  4,  are  Leap  Years. 

The  common  year  contains  52  weeks  and  1  day,  the  leap  year  52 
weeks  and  2  days.  Hence,  commonly,  each  year  begins  one  day 
later  in  the  week  than  did  the  preceding  year,  but  the  year  succeed- 
ing leap  year  begins  two  days  later. 


The  names  of  the  months,  their  abbreviations,  and  the  number 
of  days  in  each,  are  as  follows : 


January, 

31  da.     .     .     Jan. 

July,            31  da. 

.     .     July. 

February, 

28  or  29  da.    Feb. 

August,        31  da. 

.     Aug. 

March, 

31  da.     .     .     Mar. 

September,  30  da. 

.     Sept. 

April, 

30  da.     .     .     Apr. 

October,      31  da. 

.     Oct. 

May, 

31  da.     .     .     May. 

November,  30  da. 

.     Nov. 

June, 

30  da.     .     .    June. 

December,  31  da. 

.    Dec. 

UNITED   ST^ 
Ta 

lTES   MONEY 

BLE 

10  Mills  ( 

m.)=  1  Cent  .     .       f 

10  Dimes    =  1  Dollar 

.     .    $ 

10  Cents 

=  1  Dime      .     d. 

10  Dollars  =  1  Eagle 

.     .     E. 

176  TABLES  OF   DENOMINATE   NUMBERS 

ENGLISH   OR  STERLING  MONEY 

Table 

4  Farthings  (far.)  =    1  Penny     .     .     .     .    d. 

12  Pence  =    1  Shilling .     .     .     .     s. 

20  Shillings  =(^0Und'.°rj      .     .     £ 

(1  Sovereign  J 

COUNTING 
Table 

12  Things  =  1  Dozen doz. 

12  Dozen   =  1  Gross gr. 

12  Gross    =  1  Great  Gross    .     .     .     G.  gr. 
20  Things  =  1  Score. 

STATIONERY 

Table 

24  Sheets  =  1  Quire.  I         2  Reams    =  1  Bundle. 

20  Quires  =  1  Ream.  5  Bundles  =  1  Bale. 


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only 

It  Cannot  Be  Renewed 
Because  of  special  demand 



_.    «7  10A"7 

JAN  I "  tt47 

YB  35830 


54 1 325 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


